improved linear matrix inequality approach to stability analysis of linear systems with interval time varying delays this paper investigates the problem of stability analysis for a class of linear systems with interval time varying delay in order to develop a less conservative stability condition a lyapunov krasovskii functional comprising novel integral terms is introduced convex combination idea is utilized to derive a stability criterion in terms of linear matrix inequalities lmis without any additional free weighting matrices which increase drastically the computational burden of the stability test numerical examples are presented to illustrate the superiority of the proposed approach compared to some existing ones in the literature

orthogonal grid generation of an irregular region using a local polynomial collocation method abstract in this study a 2 d orthogonal grid generation model is developed by solving the governing equations of coordinate transformation with a local polynomial collocation method accompanied with the moving least squares mls approach this method was developed in a way that on the boundaries both the governing equation and boundary condition are satisfied so it is more robust and accurate than conventional collocation methods though the method used to solve the coordinate transforming equations is meshless it does not deteriorate the value of present work because most numerical models in modern use are grid dependent and grid generation of service to these models is still strongly desired particularly for finite difference models in irregular domains before applying to grid generation problems the performance of present method is tested by a bench mark potential flow problem additional to two basic grid generation problems a bottleneck problem of previous works which contains zero degree corners in the domain is carried out finally the model is applied to the orthogonal grid generation in a multi connected domain the correctness is testified by checking the orthogonality of the generated results

stability and stabilization of t s fuzzy systems with time varying delays via augmented lyapunov krasovskii functionals this paper is concerned with the problem of stability and stabilization for takagi sugeno t s fuzzy systems with time varying delays by constructing a suitable lyapunov krasovskii functional sufficient conditions for ensuring the asymptotic stability and stabilization of the concerned fuzzy systems have been derived within the framework of linear matrix inequalities lmis the advantage and effectiveness of the proposed criteria will be shown through the comparison of maximum delay bounds with some results obtained by recently published papers via four numerical examples

three dimensional solution adaptive grid generation on composite configurations the eagle 3d composite block grid code has been coupled with an implicit euler flow solver to generate solution adaptive grids for composite block configurations with an improved control function formulation the code has been tested with two complex composite configurations one of which an eight block finned body of revolution at transonic speeds is described here the solution adaptive grids obtained possess continuous slopes across block boundaries and an improved quality of aerodynamics simulation about complex geometries

fuzzy control turns 50 in 2015 we celebrate the 50th anniversary of fuzzy sets ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in fss see 1 ten years is at the same time a long period and short time thinking to the inner dynamics of research this paper presented for these 50 years of fuzzy sets is taking into account both thoughts a first part presents a quick recap of the history of fuzzy control from model free design based on human reasoning to quasi lpv linear parameter varying model based control design via some milestones and key applications the second part shows where we arrived and what the improvements are since the milestone of the first 40 years a last part is devoted to discussion and possible future research topics

on the application of the critical minimum energy subspace method to disordered systems abstract we discuss the recent application to strongly disordered systems of the critical minimum energy subspace crmes method used to limit the energy subspace of the wang landau sampling we compare with our results on the 3d random field ising model obtained by a multi range wang landau simulation over the whole energy range we point out some problems that may arise when applying the crmes scheme to models having a complex free energy landscape

efficient pseudospectral flow simulations in moderately complex geometries a computationally efficient pseudospectral method is developed for incompressible flow simulations in two dimensional geometries involving periodicity in one direction and significant surface deformations a pseudoconformal mapping is used to map the flow domain into a rectangle thereby establishing an orthogonal curvilinear coordinate system within which the governing equations are formulated the time integration of the spectrally discretized two dimensional momentum equations is performed by a second order mixed explicit implicit time integration scheme the satisfaction of the continuity equation is obtained through the solution of a poisson equation for the pressure and the use of the influence matrix technique a highly efficient iterative solver has been developed for the solution of a generalized stokes problem at each time step based on a spectrally preconditioned biconjugate gradient algorithm which exhibits almost linear scalability requiring an ordernlog2nnumber of operations wherenis the number of unknowns numerical results are presented for two dimensional steady oscillatory and peristaltic flows within an undulating channel which agree well with previous results that have appeared in the literature

robust h control of t s fuzzy systems with input time varying delays a delay partitioning method abstract addressed in this paper is the robust h control issue of t s fuzzy systems with input time varying delays by means of the delay partitioning method the delay interval is partitioned into multiple unequal subintervals whose lengths satisfy a geometric sequence on this basis a modified lyapunov krasovskii functional is presented to analyze asymptotic stability of the open loop system then a state feedback controller that ensures a prescribed h performance level for the closed loop system is proposed in linear matrix inequality format finally two numerical examples are given to illustrate the effectiveness and advantages of the obtained results

a schur complement formulation for solving free boundary stefan problems of phase change a schur complement formulation that utilizes a linear iterative solver is derived to solve a free boundary stefan problem describing steady state phase change via the isotherm newton approach which employs newton s method to simultaneously and efficiently solve for both interface and field equations this formulation is tested alongside more traditional solution strategies that employ direct or iterative linear solvers on the entire jacobian matrix for a two dimensional sample problem that discretizes the field equations using a galerkin finite element method and employs a deforming grid approach to represent the melt solid interface all methods demonstrate quadratic convergence for sufficiently accurate newton solves but the two approaches utilizing linear iterative solvers show better scaling of computational effort with problem size of these two approaches the schur formulation proves to be more robust converging with significantly smaller krylov subspaces than those required to solve the global system of equations further improvement of performance are made through approximations and preconditioning of the schur complement problem hence the new schur formulation shows promise as an affordable robust and scalable method to solve free boundary stefan problems such models are employed to study a wide array of applications including casting welding glass forming planetary mantle and glacier dynamics thermal energy storage food processing cryosurgery metallurgical solidification and crystal growth

weighted least squares method of grid generation we propose the creation of a grid smoother to improve the local grid distorsion nonsmoothness and overlapping of the transfinite interpolated grid points the second purpose of this study is to smooth the resulting grid finding through the application of the jeng and liou modified multiple one dimensional adaptive grid method

a noniterative method for the generation of orthogonal coordinates in doubly connected regions in this paper a noniterative method for the numerical generation of orthogonal curvilinear coordinates for plane annular regions between two arbitrary smooth closed curves has been developed the basic generating equation is the gaussian equation for a euclidean space under the constraint of orthogonality the resulting equation has been solved analytically for the case of isothermic coordinates a coordinate transformation then yields nonisothermic coordinates in which the outgoing coordinate can be distributed in any desired manner the method has been applied in many cases and these test results demonstrate that the proposed method can be readily applied in a variety of problems

a novel identification method for takagi sugeno fuzzy model abstract based on the xie beni index and an improved particle swarm optimization algorithm a novel identification method for the takagi sugeno fuzzy model is proposed in this paper firstly xie beni indices with a fuzzy c means clustering algorithm are adopted to find the rule number of the takagi sugeno fuzzy model by utilizing the particle swarm optimization algorithm the initial membership function and the consequent parameters of the fuzzy model are obtained in addition through an improved fuzzy c regression model and orthogonal least square method the premise structure and consequent parameters can be obtained to establish the takagi sugeno fuzzy model some well known models are used to demonstrate that the proposed method outperforms some existing methods

the random field ising model with an asymmetric trimodal probability distribution the ising model in the presence of a random field is investigated within the mean field approximation based on landau expansion the random field is drawn from the trimodal probability distribution p hi p hi h0 q hi h0 r hi where the probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution hi is the random field variable and h0 the respective strength this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays second order phase transitions which for some values of p q and h0 are followed by first order phase transitions thus confirming the existence of a tricritical point and in some cases two tricritical points also reentrance can be seen for appropriate ranges of the aforementioned variables using the variational principle we determine the equilibrium equation for magnetization solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h0

stability analysis and performance design for fuzzy model based control system under imperfect premise matching this paper investigates the stability analysis and performance design of nonlinear systems to facilitate the stability analysis the takagi sugeno t s fuzzy model is employed to represent the nonlinear plant under the imperfect premise matching in which t s fuzzy model and fuzzy controller do not share the same membership functions a fuzzy controller with enhanced design flexibility and robustness property is proposed to control the nonlinear plant however the nice characteristic given by the perfect premise matching leading to conservative stability conditions vanishes in this paper under the imperfect premise matching information of membership functions of the fuzzy model and controller are considered in stability analysis with the introduction of slack matrices relaxed linear matrix inequality lmi based stability conditions are derived using lyapunov based approach furthermore lmi based performance conditions are provided to guarantee system performance simulation examples are given to illustrate the effectiveness of the proposed approach

a numerical method for potential flows with a free surface abstract a finite difference numerical method for an accurate and efficient solution of transient potential flow problems with a free surface is described and illustrated with application to the rayleigh taylor instability and the expulsion of liquid from a pipe immersed in a tank the novel feature of the method consists of the adoption of special differentiation formulae to calculate the liquid velocity at the free surface with much greater accuracy and stability than previously possible

sampled data h fuzzy filtering for nonlinear systems with missing measurements in this paper a sampled data h fuzzy filtering problem is considered for nonlinear systems with missing measurements the nonlinear sampled data system and missing measurements are assumed to be represented by a takagisugeno ts fuzzy system and an independent identically distributed bernoulli random process respectively based on the fuzzy system the h fuzzy filtering problem is formulated to design the sampled data fuzzy filter by using the exponential mean square stability definition the stability condition with an h performance is guaranteed for the fuzzy system with the sampled data fuzzy filter and its sufficient condition is converted into the linear matrix inequality lmi format finally an example is provided to verify the effectiveness of the proposed fuzzy filtering technique

multiblock multigrid grid generation algorithms overcoming multigrid anisotropy abstract the paper presents multiblock multigrid algorithms for the generation of boundary fitted grids bfgs able to avoid undesired multigrid anisotropy arises the algorithms combine a domain decomposition technique the elliptic grid generation and the multigrid computation and provide satisfactory numerical solutions and fast convergence block matching based on two surface overlapping saves grid characteristics through the block boundaries we assume two and three dimensional generation systems allowing line spacing control and we design block by block multigrid computation to solve the transformed finite difference systems we identify anisotropy as an undesirable multigrid effect and we overcome anisotropic behaviors by investigation over coefficients of the generating systems they can provide information to select appropriate relaxation algorithms a wide series of performance evaluation results is available one block and multiblock so as one grid and multi grid algorithms have been evaluated and meaningful results are collected in tables visualizations of 2d and 3d computed grids and displays of convergence histories comparing multigrid components are shown by figures

communication delay distribution dependent networked control for a class of t s fuzzy systems this paper investigates a robust networked control for a class of takagi sugeno t s fuzzy systems the controller design specifically takes probabilistic interval distribution of the communication delay into account a general framework of networked control is first proposed the two main features are 1 the zero order hold can choose the latest control input signal when the packets received are out of order and 2 as the result of 1 the models of the all kinds of uncertainties in networked signal transfer including network induced delay and data packet dropout are under a unified framework next if the probability distribution of communication delay is known or specified in a design process sufficient stability conditions for networked t s fuzzy systems are derived which are based on the lyapunov theory following this a stabilizing controller design method is developed which shows that the solvability of the design depends not only on the upper and lower bounds of the delay but on its probability distribution as well finally a numerical example is used to show the application of the theoretical results obtained in this paper

network based output tracking control for t s fuzzy systems using an event triggered communication scheme this paper is concerned with network based output tracking control for a t s fuzzy system an event triggered communication scheme under which the threshold depends on the latest successfully transmitted sampled data is introduced to reduce network resource utilization taking the event triggered communication scheme and the asynchronous operation between the fuzzy system and the fuzzy controller the resulting system is modeled as an asynchronous threshold error dependent system with an interval time varying delay a new delay dependent criterion for l 2 gain tracking performance of the asynchronous system is derived by applying the deviation bounds of asynchronous normalized membership functions based on this performance criterion some criteria on the existence of the fuzzy tracking controller are established a co design algorithm is presented to obtain the control gains and the event triggering parameters simultaneously an example is given to illustrate the effectiveness of the proposed method

general curvilinear coordinate systems the basic ideas of the construction and use of numerically generated boundary fitted coordinate systems for the numerical solution of partial differential equations are discussed with such coordinate systems all computation can be done on a fixed square grid in the rectangular transformed region regardless of the shape or movement of the physical boundaries a number of different types of configurations for the transformed region and the basic transformation relations from a cartesian system to a general curvilinear system are given the material of this paper is applicable to all types of coordinate system generation

understanding and improving the wang landau algorithm we present a mathematical analysis of the wang landau algorithm prove its convergence and identify sources of errors and strategies for optimization in particular we found the histogram increases uniformly with small fluctuations after a stage of initial accumulation and the statistical error is found to scale as sqrt mathrm ln phantom rule 0 2em 0ex f with the modification factor f this has implications for strategies for obtaining fast convergence

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

new approach to delay dependent stability analysis and stabilization for continuous time fuzzy systems with time varying delay this paper is concerned with delay dependent stability analysis and stabilization problems for continuous time takagi and sugeno t s fuzzy systems with a time varying delay a new method for the delay dependent stability analysis and stabilization is suggested which is less conservative than other existing ones first based on a fuzzy lyapunov krasovskii functional lkf a delay dependent stability criterion is derived for the open loop fuzzy systems in the derivation process some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation and among the terms in the leibniz newton formula then a delay dependent stabilization condition based on the so called parallel distributed compensation pdc scheme is worked out for the closed loop fuzzy systems the proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities lmis and compared with the existing ones via two examples finally application to control of a truck trailer is also given to illustrate the effectiveness of the proposed design method

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

phase behavior under the averaging over disorder realizations abstract effects of the averaging over disorder realizations samples on the phase behavior are analyzed in terms of the mean field approximation for the random field ising model with infinite range interactions it is found that the averaging is equivalent to a drastic modification in the statistics of the quenched variables in its turn this lowers the critical temperature of a second order phase transition or depending on the sampling even suppresses the ordered phase possible first order transitions are shown to be softened by the sample averaging common issues and differences in the interpretation of these effects in the context of the simulation and experimental studies are discussed

applications of numerical conformal mapping abstract the application of conformal mapping methods to the solution of free surface flow problems is considered methods of numerical conformal mapping based on fourier series are extended to handle efficiently problems with time dependent boundaries they are shown to be practicable only for moderately distorted geometries extensions of the menikoff zemach method to breaking geometries are presented these latter methods are robust at quite large distortions but degrade prematurely in time dependent problems at amplitudes smaller than achieved by our recent vortex methods

delay range dependent robust stabilization for uncertain t s fuzzy control systems with interval time varying delays this paper is concerned with robust stabilization for a class of t s fuzzy control systems with interval time varying delays an approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities the main points of the approach are i two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria ii an appropriate lyapunov krasovskii functional is constructed by including both the lower and upper bounds of the interval time varying delays and iii neither model transformation nor free weighting matrices are employed in the theoretical result derivation as a result some improved sufficient stability criteria are derived and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem numerical examples are given to demonstrate the effectiveness of the proposed approach

lack of self averaging of the specific heat in the three dimensional random field ising model we apply the recently developed critical minimum energy subspace scheme for the investigation of the random field ising model we point out that this method is well suited for the study of this model the density of states is obtained via the wang landau and broad histogram methods in a unified implementation by employing the n fold version of the wang landau scheme the random fields are obtained from a bimodal distribution h i ifmmode pm else textpm fi 2 and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from l 4 to l 32 observing the finite size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat the lack of self averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above

numerical solution of poisson s equation with arbitrarily shaped boundaries using a domain decomposition and overlapping technique a direct solution scheme for numerically solving the 3 dimensional poisson s problem with arbitrarily shaped boundaries s on c1 c2n c3 on has been developed by using a boundary fitted coordinate transformation the scheme also used the technique of decomposing the closed domain into several hexahedron subdomains and then overlapping neighboring hexahedrons to deal with complicated geometries a large system of linear equations derived from discretizing the poisson s equation was solved by using a biconjugate gradient method with incomplete lu factorization of the nonsymmetric coefficient matrix as preconditioning the convergence behavior of the different domain decompositions was demonstrated for a numerical experiment application to the electrostatic field problem in the electron gun of a color picture tube confirms that the present numerical scheme should provide an efficient and convenient tool for solving many important large scale engineering problems

adaptive zoning for singular problems in two dimensions abstract winslow s method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh through simple analysis and numerical examples the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems

two dimensional unsteady euler equation solver for arbitrarily shaped flow regions a new technique is described for solving supersonic fluid dynamics problems containing multiple regions of continuous flow each bounded by a permeable or impermeable surface region boundaries are in general arbitrarily shaped and time dependent discretization of such a region for solution by conventional finite difference procedures is accomplished using an elliptic solver which alleviates the dependence on a particular base coordinate system multiple regions are coupled together through the boundary conditions the technique has been applied to a variety of problems including a shock diffraction problem and supersonic flow over a pointed ogive

the random field ising model with an asymmetric and anisotropic bimodal probability distribution abstract the ising model in the presence of a random field drawn from the asymmetric and anisotropic trimodal probability distribution p h i p h i h 0 q h i h 0 r h i is investigated the partial probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution h i is the random field variable with basic absolute value h 0 strength is the competition parameter which is the ratio between the respective strength of the random magnetic field in the two principal directions z and z and is positive so that the random fields are competing anisotropic distribution this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays mainly second order phase transitions which for some values of p q and h 0 are followed by first order phase transitions joined smoothly by a tricritical point occasionally two tricritical points appear implying another second order phase transition in addition to these points re entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of p and q using the variational principle we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0 considered as an independent variable in addition to the temperature

simple algebraic technique for nearly orthogonal grid generation rid generation is a very important aspect of solving computational fluid dynamics cfd problems where a set of partial differential equations has to be solved in a given domain it is desirable for the grid to have good orthogonality properties and the grid generator should be able to produce an arbitrary amount of clustering near the body surface when necessary generation of body fitted coordinates meeting these requirements using algebraic techniques are described by eiseman1 and smith 2 it is well known that the most efficient way of dividing the domain for external flow problems is by generating an o type grid for a twodimensional case or an o o topology grid for a three dimensional case since they give the maximum resolution near the body surface with the minimum number of grid points a simple algebraic technique has been developed for generating an o type grid or an o o topology grid for a geometry with sharp edges having a high grid density near the body surface while maintaining orthogonality the present method generates the grid by distributing spacings in the outward normal direction from a closed contour as a function of the rate of change of arc length in that direction this procedure when applied to subsequently generated contours evolves a nearly orthogonal grid with a circular outer boundary a similar procedure applied to a closed three dimensional surface produces a spherical outer boundary thereby generating an o o topology grid

calculation of interlaminar stresses in laminated plates using walsh transforms the walsh differential operator approach has much to recommend it from the point of view of computational efficiency over the standard methods for determining the interlaminar tractions from finite element displacement data as may be seen from the simplicity of the fortran routine and the ease with which the nonlinear traction tems may be modeled

a domain decomposition and overlapping method for the generation of three dimensional boundary fitted coordinate systems abstract a new method is presented for numerically generating boundary fitted coordinate systems for arbitrarily shaped three dimensional regions in the method the three dimensional region of interest is decomposed into several hexahedrons each of which has two grid surfaces overlapped with each of the neighboring hexahedrons based on this method a new computer program grid 3d has been developed which allows the generation of an unlimitted number of different types of coordinate systems application to a variety of geometries confirms that grid 3d is a convenient and efficient tool in the generation of boundary fitted coordinate systems even for a considerably complicated configuration consisting of many different components

two numerical methods for the conformal mapping of simply connected domains abstract two numerical methods are considered for the conformai mapping of a bounded simply connected domain onto the unit disc the two methods are respectively the bergman kernel method which has been described in 17 and the so called ritz method in this paper we indicate the close theoretical relationship of the two methods compare their computational efficiencies and present a number of practical applications of the approximate conformal maps

conservation form of the navier stokes equations in general nonsteady coordinates introduction r interest in the generation of general bodyoriented curvilinear coordinate systems for the purpose of solving the complete navier stokes system of equations for subsonic and supersonic flows has given rise to many forms of presentations of the equations both in conservative and nonconservative formulations based on the available solutions of the gasdynamic equations e g ref 5 the conservation law form of the equations seems definitely preferable particularly when shocks are present although the above statement cannot be repeated in a definitive sense for the case of viscous subsonic and supersonic flow prediction through the navier stokes equations nevertheless it is expected that the conservation law form may eventually be more acceptable for numerical purposes the purpose of this paper is to derive the conservation law form of the navier stokes equations in general nonsteady coordinate systems in a simple and direct fashion previous work on this subject has been done by mcvittie viviand and vinokur it will be shown in this note that the equations in the conservation law form can be obtained simply by a little manipulation of some standard vector and tensor formulas

kernel optimum nearly analytical discretization kond algorithm applied to parabolic and hyperbolic equations abstract two applications of the kernel optimum nearly analytical discretization kond algorithm to the parabolic and the hyperbolic type equations are presented in detail to lead to novel numerical schemes with very high numerical accuracy it is demonstrated numerically that the two dimensional kond p scheme for the parabolic type yields much less numerical error by over 2 3 orders measured quantitatively by the root mean square deviation from analytical solutions and reduces the cpu time to about 1 5 for a common numerical accuracy compared with the conventional explicit scheme of reference it is also demonstrated numerically that the kond h scheme for the hyperbolic type yields much less diffusive error and has fairly high stability for both of the linear and the nonlinear wave propagations compared with other conventional schemes origins of numerical errors in data processing in general numerical schemes are discussed

application of adaptive grids to fluid flow problems with asymptotic solutions proper grid point location is important in the asymptotic finite difference solution of any fluid flow or heat transfer problem this paper uses a new technique that provides a simple way of moving the mesh points in physical space in order to reduce the error in the computed asymptotic solution relative to that obtained using a fixed mesh applications to fluid flow problems are presented including boundary layer flow and inviscid supersonic flow over cylinders and wedges with associated detached shocks the treatment of curved bound aries stationary and nonstationary boundaries and systems of partial differential equations is discussed significant error reductions are demonstrated he accuracy of the finite difference solution of a partial differential equation is dependent upon the suitability of the grid used in computing the solution it is clear that two solutions to the same problem will not have equal accuracy for the same number of mesh points if the points are located differently in each case the typical grid point allocation problem in computational fluid dynamics may be stated in the following way if a solution to a set of partial differential equations is required on a physical domain subject to prescribed boundary conditions how should a fixed number of grid points be distributed in order to assure that the solution obtained is the best the term best as used here implies that some measure of error has been used in the point allocation since the size and complexity of the typical problem attempted using computational methods have in creased dramatically it is imperative that grid points be used as efficiently as possible to minimize storage requirements the construction of finite difference grid systems has received a great deal of attention over the past five years several techniques have been proposed for producing ac ceptable body fitted mesh systems probably the most well known of these methods is that of thompson et al 1 2 in which a solution of laplace s equation produces the grid in physical space this technique is ideally suited to elliptic problems where a grid point allocation can be completed at the beginning of the calculation hindman et al 3 produced an adaptive grid scheme for time dependent flows the grid speeds in physical space were obtained by using the idea proposed by thompson thames and mastin but in ad dition differentiating the equations for physical grid point location with respect to time at each time step a matrix inversion led to expressions for the components of the grid point velocity unfortunately hindman s work included only the effect of boundary motion on the grid speeds the technique used to determine grid point motion in the present study is that proposed by rai and anderson 4 the influence of both boundary motion and the details of the internal flowfield are included in the calculation of the grid point distribution numerical solutions for a number of fluid flow problems are presented showing the applicability of the technique to both viscous and inviscid flows these examples

on some relations among numerical conformal mapping methods abstract gaier and gutknecht have shown that many numerical methods for producing the conformal map from the unit disk to a simply connected region share a common theoretical basis as solutions of nonlinear integral equations arising from the hilbert transform of a function of the boundary correspondence we give a brief presentation of this classification and extend it somewhat to include some equations for the inverse correspondence such as those of menikoff and zemach noble and schwarz christoffel the use of explicit maps and the method of bisshopp are also brought into this framework an example illustrating the use of explicit maps is given

stability analysis of uniform and non uniform annular passages conducting incompressible laminar flows for small and large amplitude oscillatory motions of the outer cylinder abstract a computational method is developed involving the simultaneous integration of the navier stokes and structural equations for the purpose of studying the stability of concentric annular passages conducting incompressible laminar flows it is assumed that one side of the annulus i e the centre body is fixed and the outer cylindrical duct is flexibly supported the outer cylinder is displaced from its equilibrium position and is then released in this situation the fluid part of the problem is solved by an accurate method using a three point backward implicit scheme followed by a pseudo time iteration using an artificial compressibility factor the fluid equations are discretized in space based on a finite difference formulation and primitive variables for which stretched staggered grids are used the resulting equations are cast in delta form and are solved using an adi scheme the fluid forces acting on the vibrating cylinder are calculated from the integration of the unsteady pressure and shear stresses resulting from the unsteady primitive variables calculated the equations of motion of the structure subjected to the calculated fluid forces are solved using the runge kutta scheme to obtain the displacement of the moving cylinder the problem is solved a for small amplitude motions by means of the so called mean position mp analysis and b for large amplitude oscillations of the outer cylinder for which a time dependent coordinate transformation tdct is used to fix the computational domain both these approaches mp and tdct are applied to uniform and non uniform backstep shaped annuli for translational motion of the cylinder the problem is also solved for i rocking motion and uniform annuli and ii translational motion for diffuser shaped annuli with only mp analysis when the mp analysis is considered it is shown that for translational motion of the outer cylinder the most stable configuration is that of a uniform geometry and the least stable one is the backward step geometry for rocking motion in uniform annular geometry for some system parameters and high enough flow velocity the outer cylinder can develop flutter limit cycle oscillation the comparison between the results of mp and tdct analyses for uniform and backstep geometries for translational motion of the cylinder indicates that the outer cylinder is less stable when tdct is used and the coupled frequency of oscillation is also changed considerably

avoiding boundary effects in wang landau sampling a simple modification of the wang landau sampling algorithm removes the systematic error that occurs at the boundary of the range of energy over which the random walk takes place in the original algorithm

second order accurate boundary conditions for compressible flows the accuracy and the consistency of the methods commonly used for the numerical application of the boundary conditions on the surface of solid bodies immerged in an inviscid compressible flow is examined a new method is proposed for the application of second order accurate boundary conditions in the case of isentropic irrotational compressible flows the method is applied to a circular cylinder in uniform subsonic and low transonic flows the conservation law equations are solved using the second order accurate difference scheme of maccormack the results indicate a definite improvement over lower accuracy methods the method can be easily generalized to apply on three dimensional solid surfaces

stabilization of t s fuzzy system with time delay under sampled data control using a new looped functional this paper investigates the sampled data stabilization problem for a takagi sugeno t s fuzzy system with time delay by taking the information of states within the intervals from t k to t and t to t k 1 into account a new two side delay dependent looped functional is introduced which can not only relax the monotonic constraint of lyapunov krasovskii functional lkf but also make better use of the actual sampling pattern furthermore the sampled data fuzzy controller is designed to contain both the present and delayed state information thereby enhancing the control performance and design flexibility based on the novel augmented lkf and improved bounding technique less conservative stability criteria are derived in the form of linear matrix inequalities the superiority of proposed results is shown by two simulation examples

development of a convex polyhedral discrete element simulation framework for nvidia kepler based gpus abstract understanding the dynamical behavior of granular media gm is extremely important to many industrial processes thus simulating the dynamics of gm is critical in the design and optimization of such processes however the dynamics of gm is complex in nature and cannot be described by a closed form solution for more than a few particles a popular and successful approach in simulating the underlying dynamics of gm is by using the discrete element method dem computational viable simulations are typically restricted to a few particles with realistic complex interactions or a larger number of particles with simplified interactions this paper introduces a novel dem based particle simulation code blaze dem that is capable of simulating millions of particles on a desktop computer utilizing a nvidia kepler graphical processor unit gpu via the cuda programming model the gpu framework of blaze dem is limited to applications that require large numbers of particles with simplified interactions such as hopper flow which exhibits task level parallelism that can be exploited on the gpu blaze dem also performs real time visualization with interactive capabilities in this paper we discuss our gpu framework and validate our code by comparison between experimental and numerical hopper flow

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

an implicit boundary approach for viscous compressible high reynolds flows using a hybrid remeshed particle hydrodynamics method abstract we present an implicit boundary particle method with background mesh adaptation we use a brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high reynolds numbers a penalty term is added to the navier stokes equations to impose the boundary conditions the boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid achieving an implicit approach for flow around complex boundaries geometries simulation the main idea of the brinkman penalisation method is to model the solid obstacle as a porous medium the governing equations for the compressible fluid and penalised navier stokes for the porous medium are solved simultaneously without need for interface conditions the accuracy of the method is tested for a number of benchmark problems starting with simple cases such as a periodic laminar flow in a channel poiseuille flow to more complex problems such as the lid driven cavity with high reynolds numbers the reflection and propagation of a compressible shock wave and finally swirling flow in a model two stroke diesel engine the remeshed particle mesh method coupled with brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions

robust h control for nonlinear systems over network a piecewise analysis method a piecewise analysis method pam is proposed to investigate the h performance analysis and h control design for nonlinear networked control systems nncss which are presented in the form of t s fuzzy model with time varying input delay different from the existing method in dealing with the time varying delay the whole variation interval of the delay is divided into two subintervals with equal length respecting for the delay belonging each subinterval new criteria on h performance analysis of the nncss are obtained by checking the variation of the derivative of the lyapunov functional in the two subintervals then criteria for the h controller design are obtained by using the convexity properties of the matrix inequality and some other new analysis techniques which are shown in terms of nonlinear matrix inequalities and can be solved by using a cone complementarity liberalization method as application of the derived results h controller design is carried out for the nonlinear mass spring system discussion shows that the proposed method is less conservative than the existing references

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

an initial value approach to the production of discrete orthogonal coordinates abstract a numerical procedure is described for the orthogonalization of a discrete non orthogonal coordinate system in two dimensions one set of the non orthogonal coordinate lines is preserved by the orthogonalization procedure the other set is shifted by interpolation to form the new orthogonal system the procedure is based upon an initial value formulation with the non orthogonal coordinates as the independent variables a first order linear partial differential equation is derived which describes the orthogonal trajectories a discrete representation of the equation is suggested and an interpolation procedure is described examples of non orthogonal with orthogonalized meshes are given including closed and open coordinate lines the method may be used to generate boundary fitted coordinates for boundary value problems or eulerian time dependent codes it may also be used at each timestep in a waterbag or semi lagrangian code

boundary orthogonal biharmonic grids via preconditioned gradient methods a finite difference approximation of the biharmonic equation is solved using three preconditioned gradient methods for the generation of curvilinear boundary orthogonal grids in two dimensions the developed algorithms based on the conjugated gradient the steepest descent and the minimal residual method are applied in a number of domains of engineering interest for the purpose of comparison in terms of cpu time and number of iterations to convergence

review of some adaptive node movement techniques in finite element and finite difference solutions of partial differential equations abstract this article summarizes the results of a literature search for adaptive numerical methods of solving partial differential equations the methods discussed involve the adaptive movement of nodes so as to obtain a low level of solution truncation error while minimizing the number of nodes used in the calculation such methods are applicable to the solution of nonstationary flow problems that contain moving regions of rapid change in the flow variables surrounded by regions of relatively smooth variation flows with shock waves contact surfaces slip streams phase change interfaces and boundary layers can be modelled with great precision by these methods it will be shown that significant economies of execution can be attained if nodes are moved so that they remain concentrated in regions of rapid variation of the flow variables

wang landau study of the critical behavior of the bimodal 3d random field ising model we apply the wang landau method to the study of the critical behavior of the three dimensional random field ising model with a bimodal probability distribution for high values of the random field intensity we find that the energy probability distribution at the transition temperature is double peaked suggesting that the phase transition is first order on the other hand the transition looks continuous for low values of the field intensity in spite of the large sample to sample fluctuations observed the double peak in the probability distribution is always present for high fields

an adaptive method of lines with error control for parabolic equations of the reaction diffusion type abstract a piecewise linear finite element based method of lines is presented for the numerical solution of coupled parabolic partial differential equations which model biological and physicochemical reaction diffusion processes in one space dimension the vertial lines emanating from the space nodes in this method change at automatically selected times when in order to control a norm of the space discretization error adaptive spatial regridding occurs the regridding algorithm is an extension of one described previously by the authors 7 and is implemented in the program femol 1 which uses the lsodi package 14 15 of hindmarsh and painter to integrate the ordinary differential equations in time along the vertical lines computational results show that the method is efficient that a posteriori estimates of the space discretization error are accurate and that the adaptive procedure reliably controls the space discretization error

geometric interpretations and spatial symmetry property of metrics in the conservative form for high order finite difference schemes on moving and deforming grids the role of a geometric conservation law gcl on a finite difference scheme is revisited for conservation laws and the conservative forms of coordinate transformation metrics are introduced in general dimensions the sufficient condition of a linear high order finite difference scheme is arranged in detail for which the discretized conservative coordinate transformation metrics and jacobian satisfy the gcl identities on three dimensional moving and deforming grids subsequently the geometric interpretation of the metrics and jacobian discretized by a linear high order finite difference scheme is discussed and only the symmetric conservative forms of the discretized metrics and jacobian are shown to have the appropriate geometric structures the symmetric and asymmetric conservative forms of the metrics and jacobian are examined by the computation of an inviscid compressible fluid on highly skewed stationary and deforming grids using sixth order compact and fourth order explicit central difference schemes respectively the resolution of the isentropic vortex and the robustness of the computation are improved by employing symmetric conservative forms on the coordinate transformation metrics and jacobian that have an appropriate geometry background an integrated conservation of conservative quantities is also attained on the deforming grid when symmetric conservative forms are adopted to the time metrics and jacobian

conformal mappings for internal viscous flow problems abstract isolated occlusions in a straight channel or pipe can be described analytically in a fashion that allows efficient accurate computation of nonlinear flow fields through conformal transformations

an improved result on the stability of uncertain t s fuzzy systems with interval time varying delay this paper is concerned with the stability of uncertain t s fuzzy systems with interval time varying delay by uniformly dividing the delay interval into multiple segments and constructing an appropriate augmented lyapunov krasovskii functional some less conservative stability criteria are obtained which include some existing results as special cases since a tighter bounding inequality is employed to deal with time varying delay dependent integral items then some sources of computational complexity such as the general convex combination and free weighting matrices are not necessary to be adopted in the derivation of our results as a result the developed criteria not only theoretically improve some existing results but also have higher computational efficiency numerical examples are given to demonstrate the effectiveness of the proposed method

new approach on robust delay dependent h _ infty control for uncertain t s fuzzy systems with interval time varying delay this paper investigates the robust h infin control for takagi sugeno t s fuzzy systems with interval time varying delay by employing a new and tighter integral inequality and constructing an appropriate type of lyapunov functional delay dependent stability criteria are derived for the control problem because neither any model transformation nor free weighting matrices are employed in our theoretical derivation the developed stability criteria significantly improve and simplify the existing stability conditions also the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem numerical examples are given to demonstrate the effectiveness of the proposed methods

delay dependent h control for uncertain fuzzy systems with time varying delays this paper addresses the robust stabilization and robust h control problems of uncertain fuzzy delayed systems via a parallel distributed compensation pdc scheme the uncertainties are norm bounded and the delay may be either constant or time varying and either differentiable or non differentiable presented in this paper are some robust stabilization and robust h control criteria which are delay dependent in general and delay derivative dependent when the delay is differentiable these results enjoy much less conservatism and more computational simplicity compared with those in the existing literature and permit if the delay is differentiable the derivative to be larger than one some examples are given to illustrate the results in this paper

sampled data robust h control for t s fuzzy systems with time delay and uncertainties abstract this paper investigates sampled data robust h control for t s fuzzy systems with time delay and uncertainties by introducing the free weighting matrices to deal with the integral items and converting the coupling time varying matrix inequalities into a group of decoupling matrix inequalities an innovative delay dependent stabilization criterion is first presented then a sampled data h controller is designed to stabilize the t s fuzzy system to achieve the prescribed disturbance attenuation level which is dependent on both the size of state delay and upper bound of allowable sampling period since 1 the sawtooth structure of delay is fully considered 2 neither model transformation nor bounding techniques are employed in deriving the delay dependent results and 3 none of the integral items are arbitrarily ignored and magnified the less conservative results can be expected a practical application example is given to demonstrate the effectiveness of the proposed methods

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

the use of splines and singular functions in an integral equation method for conformal mapping we consider the integral equation method of symm for the conformal mapping of simply connected domains for the numerical solution we examine the use of spline functions of various degrees for the approximation of the source density in particular we consider ways for overcoming the difficulties associated with corner singularities for this we modify the spline approximation and in the neighborhood of each corner where a boundary singularity occurs we approximate by a function which reflects the main singular behaviour of the source density the singular functions are then blended with the splines which approximate on the remainder of the boundary so that the global approximating function has continuity of appropriate order at the transition points between the two types of approximation we show by means of numerical examples that such approximations overcome the difficulties associated with corner singularities and lead to numerical results of high accuracy

a hybrid differential algebraic method for three dimensional grid generation an effective method is presented for generating three dimensional boundary fitted grids the technique is based on a two step procedure involving the solution of differential equations and algebraic interpolations a coarse grid with an arbitrarily given point distribution at all the boundaries is first generated by solving the poisson equations with the forcing functions being automatically adjusted during the grid generation to achieve orthogonality at the boundaries a fine grid with a desired concentration of grid lines is then obtained by fitting tricubic spline functions on the coarse grid a primary feature of the method is that the mesh spacing can be quickly and explicitly changed while retaining the smoothness over the entire field and the boundary orthogonality applications to a variety of geometries demonstrate the performance of the method

discretization of free surface flows and other moving boundary problems a system of elliptic partial differential equations and boundary conditions has been developed for generating boundary fitted element discretizations of two dimensional free and moving boundary problems terms in the differential equations are scaled for dimensional homogeneity and adjustable weighting of orthogonality smoothness and concentration of the coordinate mesh they govern grid points become finite element nodes mapped isoparametrically or subparametrically from a simple or patched computational domain concentration terms contain control functions and parameters that influence node spacing along each coordinate independently overall control is by patchwise parameters and functions successful selection of these to follow deforming flow regions is straightforward and is illustrated by analysis of steady and transient slide coating flows

brief paper a discrete delay decomposition approach to stability of linear retarded and neutral systems this paper is concerned with stability of linear time delay systems of both retarded and neutral types by using some new simple quadratic lyapunov krasovskii functionals these lyapunov krasovskii functionals consist of two parts one part comes from some existing lyapunov krasovskii functionals employed in han q l 2005a absolute stability of time delay systems with sector bounded nonlinearity automatica 41 2171 2176 han q l 2005b a new delay dependent stability criterion for linear neutral systems with norm bounded uncertainties in all system matrices international journal of systems science 36 469 475 the other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments then using these new simple quadratic lyapunov krasovskii functionals some new discrete delay dependent stability criteria are derived for both retarded systems and neutral systems it is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in han 2005a and han 2005b cited above respectively numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results

robust h_ infty control for uncertain takagi sugeno fuzzy systems with interval time varying delay this paper is concerned with the problem of robust hinfin control for a class of uncertain time delay fuzzy systems the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function the takagi sugeno t s uncertain fuzzy model with interval time varying delay is adopted based on the lyapunov krasovskii functional approach some delay dependent conditions for the existence of robust hinfin controller are formulated in the form of linear matrix inequalities lmis when these lmis are feasible an hinfin controller is presented a numerical example is given to demonstrate the effectiveness of the proposed method

a mapped factored implicit scheme for the computation of duct and far field acoustics system that is boundary fitted with grid points that may be concentrated as desired on the boundary for high resolution use of such a general mapping procedure together with an explicit acoustic algorithm is described by white 3 for the analysis of noise propagation in a two dimensional variablearea duct a second objective is that the algorithm should not require excessive computer memory but at the same time should provide an accurate approximation of the acoustic field in order to satisfy these requirements a transient finite difference method together with a factored implicit procedure was chosen finally the procedure should allow the noise calculation to proceed for some distance beyond the duct exit so that an appropriate acoustic boundary condition may be specified this approach should be more accurate than terminating the calculation at the duct exit where only an approximate boundary condition can be specified also information on the noise levels and radiation patterns emanating from the duct exit will be provided in the sections that follow the algorithm is briefly described and the numerical results of a test case are presented

cubic interpolated pseudo particle method cip for solving hyperbolic type equations abstract a new cubic polynomial interpolation method where the gradient of the quantity is a free parameter is proposed for solving hyperbolic type equations various choices of the gradient are investigated and a stable and less diffusive scheme is made possible without the clipping or the flux correction procedure

numerical conformal mapping onto a rectangle with applications to the solution of laplacian problems abstract let f be the function which maps conformally a simply connected domain onto a rectangle r so that four specified points on are mapped respectively onto the four vertices of r in this paper we consider the problem of approximating the conformal map f and present a survey of the available numerical methods we also illustrate the practical significance of the conformal map by presenting a number of applications involving the solution of laplacian boundary value problems

truncation error analysis of the finite volume method for a model steady convective equation abstract a fundamental error relation inherent in the gauss divergence theorem provided the basis for studying the truncation error of the finite volume method with cell center formulation for a model steady convective equation the consistency of the classical first and second order upwind schemes are proved to be seriously dependent on the grid distribution if the simple nature of the finite volume method is retained it is found that a consistent scheme for convective terms can not avoid the dissipation due to grid nonuniformity the geometrical interpretation of the diffusive terms such as vzo are undertaken classical finite volume methods which average an undefined 0 from its neighbouring nodes are shown to introduce false fluxes whenever grid nonuniformity is present a simple modification is proposed to cancel the false fluxes two test cases for the laplace equation illustrate the applicability of the proposed scheme however even with this modified scheme the consistency problem of the diffusion term is found to be seriously dependent on the grid uniformity

robust stability and stabilization for uncertain takagi sugeno fuzzy time delay systems in this paper we consider robust stability and stabilization of uncertain takagi sugeno fuzzy time delay systems where uncertainties come into the state and input matrices some stability conditions and robust stability conditions for fuzzy time delay systems have already been obtained in the literature however those conditions are rather conservative and do not guarantee the stability and robust stability for a wide class of fuzzy systems this is true in case of designing stabilizing controllers for fuzzy time delay systems we first consider robust stability conditions of uncertain fuzzy systems conditions we obtain here are delay dependent conditions that depend on the upper bound of time delay and are given in linear matrix inequalities lmis an appropriate selection of lyapunov krasovskii function and introduction of free weighting matrices generalize robust stability conditions next we consider the stabilization problem with memoryless and delayed feedback controllers based on our generalized robust stability conditions we obtain delay dependent sufficient conditions for the closed loop system to be robustly stable and give a design method of robustly stabilizing controllers finally we give two examples that illustrate our results we compare our conditions with other stability conditions and show our conditions are rather generalized

the random field ising model with asymmetric bimodal probability distribution abstract the ising model in the presence of a random field is investigated within the mean field approximation based on landau expansion the random field is drawn from the bimodal probability distribution p h p h h 0 1 p h h 0 where the probability p assumes any value within the interval 0 1 asymmetric distribution the prevailing transitions are of second order but for some values of p and h 0 first order phase transitions take place for smaller temperatures and higher h 0 thus confirming the existence of a tricritical point also the possible reentrant phenomena in the phase diagram t h 0 plane occur for appropriate values of p and h 0 using the variational principle we determine the equilibrium equation for magnetization and solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0

on one dimensional stretching functions for finite difference calculations abstract the class of one dimensional stretching functions used in finite difference calculations is studied for solutions containing a highly localized region of rapid variation simple criteria for a stretching function are derived using a truncation error analysis these criteria are used to investigate two types of stretching functions one is an interior stretching function for which the location and slope of an interior clustering region are specified the simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine it was first employed by thomas et al aiaa j 10 1972 887 the other type of function is a two sided stretching function for which the arbitrary slopes at the two ends of the one dimensional interval are specified the simplest such general function is found to be one based on the inverse tangent the special case where the slopes were both equal and greater than one was first employed by roberts the general two sided function has many applications in the construction of finite difference grids examples of such applications are found in the listed references

fuzzy robust dynamic output feedback control of nonlinear systems with linear fractional parametric uncertainties in this paper the problem of robust dynamic output feedback control for a class of discrete time nonlinear systems with parametric uncertainties is studied the parametric uncertainties are assumed to be of a linear fractional form first the takagi sugeno t s fuzzy model is employed to represent the nonlinear system then novel approaches are developed to design the dynamic output feedback controller and sufficient conditions for robust stabilization are obtained in the form of linear matrix inequalities lmis the proposed approaches not only have abilities to effectively handle the parametric uncertainties but also are suitable for the fuzzy system with immeasurable premise variables simulation examples are presented to illustrate the design procedures and the effectiveness of the proposed methods

numerical treatment of unsteady subsonic flow past an oscillating cascade a numerical procedure for determining unsteady subsonic flow past a finite deflection oscillating cascade is described based on the assumption of small amplitu de blade motions the unsteady flow is governed by linear equations with variable coefficients which depend on the underlying steady flow these equations are solved on a nonorthogonal body fitted and periodic grid which facilitates the implementation of blade wake and cascade periodicity conditions but disallows the use of standard difference approximations instead difference approximations are based on an implicit least squares development applicable on arbitrary grids this permits flexibility in the choice of difference neighbors and the simultaneous approximations of differential equation and boundary conditions at boundary points strategies which can significantly improve numerical accuracy sample results illustrating the effects of blade thickness motion frequency and inlet mach number on the unsteady response of staggered cascades are presented n unsteady aerodynamic analysis which accounts for the effects of mean flow deflection due to blade geometry and flow turning and is capable of providing efficient predictions of unsteady response coefficients is an important requirement for turbomachinery applications a general aerodynamic model which fully includes the effects of nonuniform mean or steady flow on a small disturbance unsteady flow has been formulated and described in refs 1 and 2 the steady flow is governed by the full potential equations and the unsteady flow is governed by linear equations with variable coefficients which depend on the underlying steady flow in contrast to classical linear theory an unsteady aerodynamic formulation which includes the effects of nonuniform mean flow requires numerical solutions of the governing steady and unsteady boundary value problems numerical procedures for determining steady subsonic3 or transonic 4 potential flow through cascades are currently available a solution procedure for the linear variable coefficient unsteady problem is described in the present paper since the unsteady aerodynamic model treats realistic cascade configurations the numerical approximation must take into account nonrectangular geometries generally approximations to differential equations in nonrectangula r regions are developed in one of two ways a mapping may be defined so that in mapped variables calculation points can be placed in a rectangular grid the transformed equations are then approximated using rectangular difference expressions in the usual way alternatively more general difference ap proximations may be defined so that differential equations can be approximated on nonrectangula r meshes in physical variables thompson thames and mastin5 have defined global mappings for arbitrary two dimensional bodies but these mappings are inappropriate for cascades since the resulting meshes generally do not allow for cascade periodicity ives and liutermoza4 have determined global mappings which transform infinite two dimensional cascade regions into rectangular computational regions while allowing for cascade periodicity however the necessary mappings are not presently known for all cascades particularly those with

technical communique a delay partitioning approach to the stability analysis of discrete time systems this paper revisits the problem of stability analysis for linear discrete time systems with time varying delay in the state by utilizing the delay partitioning idea new stability criteria are proposed in terms of linear matrix inequalities lmis these conditions are developed based on a novel lyapunov functional in addition to delay dependence the obtained conditions are also dependent on the partitioning size we have also established that the conservatism of the conditions is a non increasing function of the number of partitions numerical examples are given to illustrate the effectiveness and advantage of the proposed methods