a 6th order staggered compact finite difference method for the incompressible navier stokes and scalar transport equations in a previous paper we have developed a staggered compact finite difference method for the compressible navier stokes equations in this paper we will extend this method to the case of incompressible navier stokes equations in an incompressible flow conservation of mass is ensured by the well known pressure correction method 7 21 the advection and diffusion terms are discretized with 6th order spatial accuracy the discrete poisson equation which has to be solved in the pressure correction step has the same spatial accuracy as the advection and diffusion operators the equations are integrated in time with a third order adams bashforth method results are presented for a 1d advection diffusion equation a 2d lid driven cavity at a reynolds number of 1000 and 10 000 and finally a 3d fully developed turbulent duct flow at a bulk reynolds number of 5400 in all cases the methods show excellent agreement with analytical and other numerical and experimental work

continuous takagi sugeno s models reduction of the number of lmi conditions in various fuzzy control design technics fuzzy models of the takagi sugeno type enable representation of a wide class of nonlinear models conditions about their stabilization can be derived systematically usually these conditions are written as linear matrix inequality lmi problems in this paper we use a collection of properties concerning matrices to extend the area of solutions involving the feedback control laws we will work out with continuous fuzzy models and supply results about the stabilization the regulator problem and also hinfin control solutions based on a reduced number of decision variables implying a reduced number of lmi conditions are also proposed we show that a good tradeoff can been obtained

accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

adaptive fuzzy output feedback control for output constrained nonlinear systems in the presence of input saturation abstract in this paper the problem of adaptive fuzzy output feedback control is investigated for a class of output constrained uncertain nonlinear systems with input saturation and unmeasured states to address output constraint and input constraint a barrier lyapunov function and an auxiliary design system are employed respectively fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is designed to estimate the unmeasured states by utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design an observer based adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that all the signals in the closed loop system are bounded and the input and output constraints are circumvented simultaneously a numerical example is provided to illustrate the effectiveness of the proposed approach

nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time ts fuzzy models a new approach the discrete time uncertain nonlinear models are considered in a takagi sugeno form and their stabilization is studied through a non quadratic lyapunov function the classical conditions consider a one sample variation here the main results are obtained considering k samples variation i e deltak v x t v x t k v x t the results are shown to always include the classical cases and several examples illustrate the effectiveness of the approach

numerical investigation on the stability of singular driven cavity flow by applying the singularity subtraction technique to the unsteady driven cavity problem the stability of the impulsively started flow is investigated without smoothing the corner singularity a second order spectral projection method allows localization of the critical reynolds number for the first hopf bifurcation in the interval 8017 6 8018 8

technical communique improvement on observer based h control for t s fuzzy systems this paper provides an improved result over that in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582 for the problem of observer based h control for nonlinear systems in takagi sugeno t s fuzzy model it contributes in three aspects i the present result is less conservative than that in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582 ii the present strict lmi method is a single step approach which overcomes the drawback of a two step approach in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582 iii the matrix dimensions are largely reduced compared with the corresponding ones in liu and zhang 2003 new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 1571 1582

improved h control of discrete time fuzzy systems a cone complementarity linearization approach in this paper new results are presented for h analysis and synthesis problems of discrete time takagi sugeno ts fuzzy systems by defining a multiple lyapunov function a new sufficient condition guaranteeing the h performance of the ts fuzzy systems is first derived which is expressed by a set of linear matrix inequalities lmis both theoretical analysis and numerical examples show that such a new condition is less conservative than previous results obtained within the quadratic framework based on this new condition for h performance the corresponding h controller design problem is then investigated different from the traditional quadratic framework the synthesis problem is solved by exploiting the cone complementarity linearization ccl method together with a sequential minimization problem subject to lmi constraints obtained for the existence of admissible controllers which can be readily solved by using standard numerical software

design of a polynomial fuzzy observer controller with sampled output measurements for nonlinear systems considering unmeasurable premise variables in this paper we propose a polynomial fuzzy observer controller for nonlinear systems where the design is achieved through the stability analysis of polynomial fuzzy model based pfmb observer control system the polynomial fuzzy observer estimates the system states using estimated premise variables the estimated states are then employed by the polynomial fuzzy controller for the feedback control of nonlinear systems represented by the polynomial fuzzy model the system stability of the pfmb observer control system is analyzed based on the lyapunov stability theory although using estimated premise variables in polynomial fuzzy observer can handle a wider class of nonlinear systems it leads to a significant drawback that the stability conditions obtained are nonconvex matrix decoupling technique is employed to achieve convex stability conditions in the form of sum of squares we further extend the design and analysis to polynomial fuzzy observer controller using a sampled data technique for nonlinear systems where only sampled output measurements are available simulation examples are presented to demonstrate the feasibility and validity of the design and analysis results

error dynamics the propagation of a signal in a continuous medium and the associated evolution of error is of prime importance in many applications of applied physics there have been many efforts in analyzing error dynamics using method attributed to von neumann 1 2 that is readily applied for linear equations and in quasilinearized form for non linear equations the main assumption for linear problems is that the error and the signal follow the same dynamics while this appears intuitively correct the main aim behind this work is to show that this is not correct for discrete computing due to dispersion or phase error or when the numerical method is not strictly neutrally stable we demonstrate the above with the help of the linear advection equation for the analysis of space time discretization schemes the linear advection equation as a model that represents many flows and wave phenomena is used

stable and accurate pressure approximation for unsteady incompressible viscous flow how to properly specify boundary conditions for pressure is a longstanding problem for the incompressible navier stokes equations with no slip boundary conditions an analytical resolution of this issue stems from a recently developed formula for the pressure in terms of the commutator of the laplacian and leray projection operators here we make use of this formula to a improve the accuracy of computing pressure in two kinds of existing time discrete projection methods implicit in viscosity only and b devise new higher order accurate time discrete projection methods that extend a slip correction idea behind the well known finite difference scheme of kim and moin we test these schemes for stability and accuracy using various combinations of c 0 finite elements for all three kinds of time discretization one can obtain third order accuracy for both pressure and velocity without a time step stability restriction of diffusive type furthermore two kinds of projection methods are found stable using piecewise linear elements for both velocity and pressure

robust static output feedback h control for uncertain fuzzy systems this paper will focus on robust static output feedback sof h control for discrete time takagi sugeno t s fuzzy systems with time varying norm bounded uncertainties first a new h performance analysis criterion is proposed for the fuzzy systems then sufficient conditions for designing fuzzy sof h controllers are given in terms of solutions to a set of linear matrix inequalities lmis in contrast to the existing methods for designing the sof h controllers the output matrices of the considered fuzzy system are allowed to be non common and to have uncertainties moreover theoretical proof is given to show that the proposed design conditions include some existing results as special cases simulation examples are provided to show the effectiveness of the proposed design method

observer design of discrete time t s fuzzy systems via multi instant homogenous matrix polynomials this paper is concerned with the design of observer for discrete time nonlinear systems in the takagi sugeno t s fuzzy form under the framework of multi instant homogenous matrix polynomials a novel fuzzy observer and a new lyapunov function which are homogenous polynomially parameter dependent on both the current time normalized fuzzy weighting functions and the m steps past time normalized fuzzy weighting functions are proposed for conceiving less conservative observer design conditions since the algebraic properties of both the current time normalized fuzzy weighting functions and the m steps past time normal ized fuzzy weighting functions are fully considered the relaxation quality of the fuzzy observer design of discrete time t s fuzzy systems is significantly improved in particular some existing fuzzy lyapunov functions and fuzzy observers are special cases of the lyapunov function and the fuzzy observer given in this paper respectively finally a numerical example is provided to illustrate the effectiveness of the proposed approach index terms discrete time system homogenous matrix polynomials multi instant observer design takagi sugeno t s fuzzy model

lmi based approach for output feedback stabilization for discrete time takagi sugeno systems static output feedback stabilizing controllers for nonlinear systems represented by discrete time takagi sugeno fuzzy models are studied the main result concerns the stabilization based on the parallel distributed compensation pdc approach sufficient conditions are provided for quadratic and nonquadratic stability to design static output feedback stabilizing controllers a numerical procedure based on the cone complementarity algorithm is given it is shown that the relaxed conditions proposed in the nonquadratic case outperform those for the quadratic case two numerical examples are given to illustrate the efficiency of the proposed approach

an efficient method for the incompressible navier stokes equations on irregular domains with no slip boundary conditions high order up to the boundary common efficient schemes for the incompressible navier stokes equations such as projection or fractional step methods have limited temporal accuracy as a result of matrix splitting errors or introduce errors near the domain boundaries which destroy uniform convergence to the solution in this paper we recast the incompressible constant density navier stokes equations with the velocity prescribed at the boundary as an equivalent system for the primary variables velocity and pressure equation for the pressure the key difference from the usual approaches occurs at the boundaries where we use boundary conditions that unequivocally allow the pressure to be recovered from knowledge of the velocity at any fixed time this avoids the common difficulty of an apparently over determined poisson problem since in this alternative formulation the pressure can be accurately and efficiently recovered from the velocity the recast equations are ideal for numerical marching methods the new system can be discretized using a variety of methods including semi implicit treatments of viscosity and in principle to any desired order of accuracy in this work we illustrate the approach with a 2 d second order finite difference scheme on a cartesian grid and devise an algorithm to solve the equations on domains with curved non conforming boundaries including a case with a non trivial topology a circular obstruction inside the domain this algorithm achieves second order accuracy in the l norm for both the velocity and the pressure the scheme has a natural extension to 3 d

observer based robust h sub spl infin control for fuzzy systems using two step procedure this paper investigates both robust h sub spl infin analysis and synthesis problems involving observer based fuzzy control via linear matrix inequality methods for which efficient optimization techniques are available the observer and controller are capable of disturbance rejection in the presence of unknown but bounded disturbance we present results in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are demonstrated by examples

compact finite difference scheme and rbf meshless approach for solving 2d rayleigh stokes problem for a heated generalized second grade fluid with fractional derivatives abstract this article is devoted to the comparison between a high order difference scheme and radial basis functions rbfs meshless approach for the numerical solution of two dimensional fractional rayleigh stokes problem the fractional derivative of problem is described in the riemann liouville sense in the high order difference scheme we discretize the spaces derivatives with a fourth order compact scheme and use the grunwald letnikov discretization of the riemann liouville derivatives to obtain a fully discrete implicit scheme also in the rbf meshless method we discretize the time fractional derivatives of the mentioned equation by integrating both sides of it then we will use the kansa s approach to approximate the spatial derivatives we prove the stability and convergence for high order difference scheme using fourier analysis and for time discrete scheme in rbf method via energy approach we compare the results of compact finite difference method and rbf meshless approach in terms of accuracy and cpu time also we compare the numerical results of compact difference scheme with other methods in the literature to show the high accuracy and efficiency of the proposed method

multiparameter full waveform inversion marine and land examples seismic full waveform inversion fwi as proposed by lailly and tarantola in the 1980s lailly 1983 tarantola 1987 consists of minimizing the misfit between observed and computed data this data fitting approach is attractive because theoretically it allows us to directly invert for the earth parameters without using concepts like angle reflectivity and scale separation between background velocity and reflectivity however the applicability of waveform inversion is limited by at least two factors the numerical cost of the solutions of the elastodynamic equations needed to obtain the computed data and the ill posedness of the inverse problem because of the presence of local minima caused by cycle skipping between observed and computed data the large increase in computing power became an enabler for this technique even if it is still expensive to numerically solve the visco elastic wave equations and most of the current waveform inversion implementations make severe approximations notably the

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

a dispersion relation preserving optimized upwind compact difference scheme for high accuracy flow simulations in this work we have derived an optimized upwind compact difference scheme for achieving excellent spatial resolution the derived numerical scheme adds numerical diffusion which is strictly restricted to a high wavenumber region in order to control numerical instabilities as well as to achieve de aliasing ability more importantly the derived numerical scheme has excellent dispersion relation preserving drp property the applicability of the proposed scheme in simulating real flow problems has been demonstrated by solving flow inside a lid driven cavity a transitional flow past ag24 aerofoil and a two dimensional decaying turbulence flow

further studies on control synthesis of discrete time t s fuzzy systems via useful matrix equalities this paper is concerned with further studies on the control synthesis of discrete time nonlinear systems in the takagi sugeno t s fuzzy form to do this a novel slack variable technique is presented by developing some useful matrix equalities which are homogenous polynomially parameter dependent on both the current time normalized fuzzy weighting functions and the past time normalized fuzzy weighting functions under the framework of homogenous matrix polynomials the algebraic properties of both the current time normalized fuzzy weighting functions and the past time normalized fuzzy weighting functions are collected for the first time into sets of united collection matrices consequently the relaxation quality of control synthesis of discrete time t s fuzzy systems is improved i e the convergence of asymptotically necessary and sufficient stabilization conditions is further sped up finally a numerical example is provided to illustrate the effectiveness of the proposed result

robust reliable h control for fuzzy systems with random delays and linear fractional uncertainties this article studies the reliable robust stabilization problem for a class of uncertain takagi sugeno ts fuzzy systems with time varying delays the delay factor is assumed to be random delay which belongs to a given interval and parameter uncertainties are considered with linear fractional transformation form by implementing a proper novel lyapunov functional together with linear matrix inequality lmi approach a new set of delay dependent sufficient conditions is derived to guarantee the asymptotic stability of ts fuzzy system with a prescribed h performance index further a reliable robust h control design with an appropriate gain matrix has been derived to achieve the robust asymptotic stability for uncertain ts fuzzy system further schur complement and jensen s integral inequality are used to simplify the derivation in the main results the set of sufficient conditions is established using the relationship among the random time varying delay and its lower and upper bounds which can be easily solved by matlab lmi toolbox finally an illustrative example based on the truck trailer model is provided to show the effectiveness of the proposed new design technique

inversion of normal incidence seismograms the well known instability of kunetz s 1963 inversion algorithm can be explained by the progressive manner in which the calculations are done descending from the surface and by the fact that completely different impedances can yield indistinguishable synthetic seismograms those difficulties can be overcome by using an iterative algorithm for the inversion of the one dimensional 1 d wave equation together with a stabilizing constraint on the sums of the jumps of the desired impedance for computational efficiency the synthetic seismogram is computed by the method of characteristics and the gradient of the error criterion is computed by optimal control techniques adjoint state equation the numerical results on simulated data confirm the expected stability of the algorithm in the presence of measurement noise tests include noise levels of 50 percent the inversion of two field sections demonstrates the practical feasibility of the method and the importance of taking into account all internal a

existence of similarity transformation converting bmis to lmis under a mild condition we investigate the existence of a similarity transformation regarding robust hinfin stability analysis and observer controller synthesis problems the observer based controller is capable of disturbance rejection in the presence of unknown but bounded disturbance we present results which illustrate plainly the role of the similarity transformation in converting a bmi problem into an lmi problem in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are illuminated by examples

controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a kind of controller synthesis method for fuzzy dynamic systems based on a piecewise smooth lyapunov function the basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the control laws can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software an example is given to illustrate the application of the proposed methods

a robust and accurate outflow boundary condition for incompressible flow simulations on severely truncated unbounded domains we present a robust and accurate outflow boundary condition and an associated numerical algorithm for incompressible flow simulations on unbounded physical domains aiming at maximizing the domain truncation without adversely affecting the flow physics the proposed outflow boundary condition allows for the influx of kinetic energy into the domain through the outflow boundaries and prevents un controlled growth in the energy of the domain in such situations the numerical algorithm for the outflow boundary condition is developed on top of a rotational velocity correction type strategy to de couple the pressure and velocity computations and a special construction in the algorithmic formulation prevents the numerical locking at the outflow boundaries for time dependent problems extensive numerical tests for flow problems with bounded and semi bounded physical domains demonstrate that this outflow boundary condition and the numerical algorithm produce stable and accurate simulations on even severely truncated computational domains where strong vortices may be present at or exit the outflow boundaries the method developed herein has the potential to significantly expedite simulations of incompressible flows involving outflow or open boundaries and to enable such simulations at reynolds numbers significantly higher than the state of the art

analysis of a new high resolution upwind compact scheme a new high resolution upwind compact scheme is presented and analyzed along with several previously proposed schemes for numerical dispersion dissipation anisotropy phase damping dispersion relation preservation property and numerical stability the schemes are tested on problems of the propagation of a initially discontinuous wave and of the transport of a sharp scalar cone a benchmark problem of aeroacoustics is solved with the present scheme giving satisfactory resolution the scheme compares well with the existing schemes for the range of properties considered desirable in high resolution schemes

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

a descriptor representation approach to observer based h control synthesis for discrete time fuzzy systems this work is concerned with the observer based h control synthesis problem of discrete time takagi sugeno t s fuzzy systems with external disturbances the objective is to find a new way to design the controller and observer guaranteeing a prescribed h performance of the fuzzy system by the descriptor representation approach two new conditions for observer based h control synthesis are proposed based on various lyapunov function candidates which are in the form of linear matrix inequalities lmis a numerical example will be given to show the efficiency of the proposed method

static output feedback h control of a class of nonlinear discrete time systems this paper is concerned with the problem of designing robust h static output feedback sof controllers for a class of discrete time nonlinear systems which are represented by t s fuzzy models by considering the properties of system output matrices a method for h sof control synthesis is developed in terms of solutions to a set of linear matrix inequalities lmis in contrast to the existing techniques for designing sof controllers the new proposed method can give less conservative results by removing the constraint that the considered lyapunov matrix is diagonal numerical examples are given to illustrate the effectiveness of the proposed design method

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems this paper proposes a new quadratic stabilization condition for takagi sugeno t s fuzzy control systems the condition is represented in the form of linear matrix inequalities lmis and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature a rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases in comparison with conventional conditions the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design the latter design work is quite hard for t s fuzzy control systems based on the lmi based conditions derived one can easily synthesize controllers for stabilizing t s fuzzy control systems since only a set of lmis is involved the controller design is quite simple and numerically tractable finally the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous time nonlinear system

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

analysis of central and upwind compact schemes central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space numerical stability and dispersion relation preservation a von neumann matrix spectral analysis is developed here to analyze spatial discretization schemes for any explicit and implicit schemes to investigate the full domain simultaneously this allows one to evaluate various boundary closures and their effects on the domain interior the same method can be used for stability analysis performed for the semi discrete initial boundary value problems ibvp this analysis tells one about the stability for every resolved length scale some well known compact schemes that were found to be g k s and time stable are shown here to be unstable for selective length scales by this analysis this is attributed to boundary closure and we suggest special boundary treatment to remove this shortcoming to demonstrate the asymptotic stability of the resultant schemes numerical solution of the wave equation is compared with analytical solution furthermore some of these schemes are used to solve two dimensional navier stokes equation and a computational acoustic problem to check their ability to solve problems for long time it is found that those schemes that were found unstable for the wave equation are unsuitable for solving incompressible navier stokes equation in contrast the proposed compact schemes with improved boundary closure and an explicit higher order upwind scheme produced correct results the numerical solution for the acoustic problem is compared with the exact solution and the quality of the match shows that the used compact scheme has the requisite drp property

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

a new combined stable and dispersion relation preserving compact scheme for non periodic problems a new compact scheme is presented for computing wave propagation problems and navier stokes equation a combined compact difference scheme is developed for non periodic problems called nccd henceforth that simultaneously evaluates first and second derivatives improving an existing combined compact difference ccd scheme following the methodologies in sengupta et al t k sengupta s k sircar a dipankar high accuracy schemes for dns and acoustics j sci comput 26 2 2006 151 193 stability and dispersion relation preservation drp property analysis is performed here for general ccd schemes for the first time emphasizing their utility in uni and bi directional wave propagation problems that is relevant to acoustic wave propagation problems we highlight a specific points in parameter space those give rise to least phase and dispersion errors for non periodic wave problems b the solution error of ccd nccd schemes in solving stommel ocean model an elliptic p d e and c the effectiveness of the nccd scheme in solving navier stokes equation for the benchmark lid driven cavity problem at high reynolds numbers showing that the present method is capable of providing very accurate solution using far fewer points as compared to existing solutions in the literature

robust h fuzzy static output feedback control of t s fuzzy systems with parametric uncertainties this paper addresses robust h fuzzy static output feedback control problem for t s fuzzy systems with time varying norm bounded uncertainties sufficient conditions for synthesis of a fuzzy static output feedback controller for t s fuzzy systems are derived in terms of a set of linear matrix inequalities lmis in comparison with the existing literatures the proposed approach not only simplifies the design procedure but also achieves a better h performance three drawbacks existing in the previous papers such as coordinate transformation same output matrices and bmi problem have been eliminated the effectiveness of the proposed design method is demonstrated by an example for the control of a truck trailer system

a novel approach to h_ bm infty decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h infin decentralized output feedback controller for nonlinear interconnected systems this study introduces h infin decentralized fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear interconnected systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables only a novel decoupled method is proposed in this study to transform the non linear matrix inequality non lmi conditions into some lmi forms by the proposed decoupled method the problem of h infin decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp with five prespecified scalars for each subsystem in general it is a difficult task to solve the evp with five prespecified scalars fortunately this special evp can be easily solved by using a genetic algorithm and an lmi based optimization method finally a simulation example is given to illustrate the design procedure and robust performance of the proposed methods

further improvement and analysis of ccd scheme dissipation discretization and de aliasing properties in this paper we further analyze a combined compact difference ccd scheme proposed recently t k sengupta v lakshmanan v v s n vijay a new combined stable and dispersion relation preserving compact scheme for non periodic problems j comput phys 228 8 2009 3048 3071 for its dissipation discretization properties to show that its superiority also helps in controlling aliasing error for a benchmark internal flow however application of the same ccd method to study the receptivity of a boundary layer experiencing adverse pressure gradient is not successful this is traced to the nature of the equilibrium flow where the better dissipation property is not helpful in the inviscid part of the flow where the aliasing problems continue to persist a further modification is proposed to the ccd method here to solve complex physical problems requiring information on higher order disturbance quantities as in problems of flow receptivity and instability

fuzzy modeling and h control for general 2d nonlinear systems this paper investigates h control for general 2d nonlinear systems based on a 2d takagi sugeno t s fuzzy model the system under consideration is an extension of the general 2d linear system to a nonlinear case taking the spatial and structural features into consideration a 2d t s fuzzy model is first established in designing the h controller the inputs are regarded as variables independent from the states and then basis dependent free matrices are introduced it has been shown that separation of the input and state variables does not lead to any conservativeness compared with the commonly used method thus a fuzzy h controller is designed using a common free matrix resulting in only r linear matrix inequalities the computational advantage is obvious for fuzzy systems with a large number of fuzzy rules we also demonstrate that the proposed method is less computationally expensive than the approach in which the input variable state variable and its forward stepping state are all separately considered although these two methods can achieve the same optimal h performance simulation examples are used to demonstrate the technique and its advantages

h_ bm infty fuzzy filtering of nonlinear systems with intermittent measurements this paper is concerned with the problem of h infin fuzzy filtering of nonlinear systems with intermittent measurements the nonlinear plant is represented by a takagi sugeno t s fuzzy model the measurements transmission from the plant to the filter is assumed to be imperfect and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the phenomenon of the missing measurements attention is focused on the design of an h infin filter such that the filter error system is stochastically stable and preserves a guaranteed h infin performance a basis dependent lyapunov function approach is developed to design the h infin filter by introducing some slack matrix variables the coupling between the lyapunov matrix and the system matrices is eliminated which greatly facilitates the filter design procedure the developed theoretical results are in the form of linear matrix inequalities lmis finally an illustrative example is provided to show the effectiveness of the proposed approach

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

two dimensional nonlinear inversion of seismic waveforms numerical results the nonlinear problem of inversion of seismic waveforms can be set up using least squares methods the inverse problem is then reduced to the problem of minimizing a lp nonquadratic function in a space of many 104to106 variables using gradient methods leads to iterative algorithms each iteration implying a forward propagation generated by the actual sources a backward propagation generated by the data residuals acting as if they were sources and a correlation at each point of the space of the two fields thus obtained which gives the updated model the quality of the results of any inverse method depends heavily on the realism of the forward modeling finite difference schemes are a good choice relative to realism because although they are time consuming they give excellent results numerical tests performed with multioffset synthetic data from a two dimensional model prove the feasibility of the approach if only surface recorded reflections are used the high spatial frequency content of the

a new fuzzy lyapunov function approach for a takagi sugeno fuzzy control system design in this paper a new fuzzy lyapunov function approach is presented for a class of continuous time takagi sugeno fuzzy control system the proposed fuzzy lyapunov function is formulated as a line integral of a fuzzy vector which is a function of the state and it can be regarded as the work done from the origin to the current state in the fuzzy vector field unlike the approaches using a fuzzy blending of multiple quadratic lyapunov functions the time derivatives of membership functions do not appear in the proposed approach the effectiveness of the proposed approach is shown through numerical examples

observer based robust fuzzy control of nonlinear systems with parametric uncertainties this paper addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties and the state variables unavailable for measurement the takagi sugeno t s fuzzy model system with parametric uncertainties is adopted for modeling the nonlinear system and establishing fuzzy state observer sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability and are formulated in the format of linear matrix inequalities lmis the effectiveness of the proposed fuzzy controller and fuzzy observer design methodology is finally demonstrated through numerical simulations on an inverted pendulum system

conditioning the full waveform inversion gradient to welcome anisotropy abstractmultiparameter full waveform inversion fwi suffers from complex nonlinearity in the objective function compounded by the eventual trade off between the model parameters a hierarchical approach based on frequency and arrival time data decimation to maneuver the complex nonlinearity associated with this problem usually falls short in anisotropic media in place of data decimation i use a model gradient filter approach to access the parts of the gradient more suitable to combat the potential nonlinearity and parameter trade off the filter is based on representing the gradient in the time lag normalized domain in which small scattering angles of the gradient update are initially muted out the model update hierarchical filtering strategy include applying varying degrees of filtering to the different anisotropic parameter updates a feature not easily accessible to simple data decimation using fwi and reflection based fwi when the modeled data are obtained with the single scattering theory al

observer based relaxed cal h _ infty control for fuzzy systems using a multiple lyapunov function this short paper proposes a method of designing a fuzzy observer based h infin controller for discrete time takagi sugeno t s fuzzy systems to enhance the applicability of the output feedback controller and improve its performance this short paper first builds a set of fuzzy control rules with premise variables different from those of the t s fuzzy system and sets the overall controller to be dependent on not only the current time but also the one step past information on the estimated fuzzy weighting functions then based on the fuzzy control rules this short paper establishes a less conservative h infin stabilization condition incorporated with a multiple lyapunov function dependent on the estimated fuzzy weighting functions through a two step design procedure the h infin stabilization condition is formulated in terms of parameterized linear matrix equalities plmis which are reconverted into lmis with the help of an efficient and effective relaxation scheme

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

a three point combined compact difference scheme a new three point combined compact difference ccd scheme is developed for numerical models the major features of the ccd scheme are three point implicit sixth order accuracy and inclusion of boundary values due to its combination of the first and second derivatives the ccd scheme becomes more compact and more accurate than normal compact difference schemes the efficient twin tridiagonal for calculating derivatives and triple tridiagonal for solving partial difference equation with the ccd scheme methods are also presented besides the ccd scheme has sixth order accuracy at periodic boundaries and fifth order accuracy at nonperiodic boundaries the possibility of extending to a three point eighth order scheme is also included

compact finite difference schemes with high accuracy for one dimensional nonlinear schrodinger equation abstract in this paper two compact finite difference schemes are presented for the numerical solution of the one dimensional nonlinear schrodinger equation the discrete l 2 norm error estimates show that convergence rates of the present schemes are of order o h 4 2 numerical experiments on some model problems show that the present schemes preserve the conservation laws of charge and energy and are of high accuracy

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

output feedback lmi tracking control conditions with h criterion for uncertain and disturbed t s models this work concerns the tracking problem of uncertain takagi sugeno t s continuous fuzzy model with external disturbances the objective is to get a model reference based output feedback tracking control law the control scheme is based on a pdc structure a fuzzy observer and a h performance to attenuate the external disturbances the stability of the whole closed loop model is investigated using the well known quadratic lyapunov function the key point of the proposed approaches is to achieve conditions under a lmi linear matrix inequalities formulation in the case of an uncertain and disturbed t s fuzzy model this formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems finally a simulation is provided on the well known inverted pendulum testbed to show the efficiency of the proposed approach

a systematic approach to improve multiple lyapunov function stability and stabilization conditions for fuzzy systems this paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for takagi sugeno ts systems this approach is based on the idea of multiple lyapunov functions together with simple techniques for introducing slack matrices unlike some previous approaches based on multiple lyapunov functions both the stability and the stabilization conditions are written as linear matrix inequality lmi problems the proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the lmi problems numeric examples illustrate the effectiveness of this method

robust nonfragile h_ infty filtering of fuzzy systems with linear fractional parametric uncertainties this paper is concerned with the h filtering problem for continuous time takagi sugeno t s fuzzy systems different from existing results for fuzzy h filtering the proposed ones are toward uncertain fuzzy systems with linear fractional parametric uncertainties attention is focused on the design of a fuzzy filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by a descriptor representation approach two sufficient conditions for the h filter design are proposed in terms of linear matrix inequalities lmis when these lmis are feasible an explicit expression of the desired filter is given a simulation example will be given to show the efficiency of the proposed methods

conditions of output stabilization for nonlinear models in the takagi sugeno s form this paper deals with the control law design with an observer for models in the takagi sugeno s ts form in the general case where the nonlinearities and the variables involved are not measurable the results presented in this paper give sufficient conditions of stabilization for the global loop i e ts model stabilized with a state feedback and a fuzzy observer conditions are given in the form of linear matrix inequalities lmi problem

design of polynomial fuzzy observer controller with membership functions using unmeasurable premise variables for nonlinear systems in this paper the stability of polynomial fuzzy model based pfmb observer control system is investigated via lyapunov stability theory the polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states then the estimated system states are used for the state feedback control of nonlinear systems although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the fuzzy model based fmb control strategy it leads to non convex stability conditions therefore the refined completing square approach is proposed to derive convex stability conditions in the form of sum of squares sos with less manually designed parameters in addition the membership functions of the polynomial observer controller are optimized by the improved gradient descent method which outperforms the widely applied parallel distributed compensation pdc approach according to a general performance index simulation examples are provided to verify the proposed design and optimization scheme

a three point sixth order nonuniform combined compact difference scheme a three point nonuniform combined compact difference nccd scheme with sixth order accuracy is proposed for numerical models the nccd scheme is a generalization of the previously proposed combined compact difference ccd scheme with a global hermitan polynomial spline and has major improved features such as error and computational cpu time reduction for nonperiodic boundaries additional sixth or fifth order nonuniform boundary conditions are proposed the nccd scheme with either sixth or fifth order additional boundary conditions can increase the accuracy and decrease the cpu time about 1 2 orders of magnitude compared to the ccd scheme

new delay dependent stabilization conditions of t s fuzzy systems with constant delay this paper focuses on the problem of robust control for takagi sugeno t s fuzzy systems with time delay the delay dependent stability analysis and controller synthesis have been addressed the free weighting matrix method has been used for stability analysis and controller synthesis new and less conservative delay dependent stability conditions are proposed in terms of linear matrix inequalities lmi finally some examples are given to illustrate the effectiveness of the proposed approaches

robust h control of takagi sugeno fuzzy systems with state and input time delays this paper addresses the robust h fuzzy control problem for nonlinear uncertain systems with state and input time delays through takagi sugeno t s fuzzy model approach the delays are assumed to be interval time varying delays and no restriction is imposed on the derivative of time delay based on lyapunov krasoviskii functional method delay dependent sufficient conditions for the existence of an h controller are proposed in linear matrix inequality lmi format illustrative examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology

derivation of high order compact finite difference schemes for non uniform grid using polynomial interpolation in this paper simple polynomial interpolation is used to derive arbitrarily high order compact schemes for the first derivative and tridiagonal compact schemes for the second derivative consisting of three second derivative nodes in the interior and two on the boundary on non uniform grids boundary and near boundary schemes of the same order as the interior are also developed using polynomial interpolation and for a general compact scheme on a non uniform grid it is shown that polynomial interpolation is more efficient than the conventional method of undetermined coefficients for finding coefficients of the scheme the high order non uniform schemes along with boundary closure of up to 14th order thus obtained are shown to be stable on a non uniform grid with appropriate stretching so that more grid points are clustered near the boundary the stability and resolution properties of the high order non uniform grid schemes are studied and the results of three numerical tests on stability and accuracy properties are also presented

relaxed stabilization conditions for continuous time takagi sugeno fuzzy control systems this paper deals with the stabilization of continuous time takagi sugeno t s fuzzy control systems based on fuzzy lyapunov functions and nonparallel distributed compensation non pdc control laws new stabilization conditions are represented in the form of linear matrix inequalities lmis the theoretical proof shows that the proposed conditions can provide less conservatism than the existing results in the literature moreover in order to demonstrate the effectiveness of the non pdc control laws the problem of h controller design for t s fuzzy systems is also studied simulation examples are given to illustrate the merits of the proposed methods

a descriptor system approach to fuzzy control system design via fuzzy lyapunov functions there has been a flurry of research activities in the analysis and design of fuzzy control systems based on linear matrix inequalities lmis this paper presents a descriptor system approach to fuzzy control system design using fuzzy lyapunov functions the design conditions are still cast in terms of lmis but the proposed approach takes advantage of the redundancy of descriptor systems to reduce the number of lmi conditions which leads to less computational requirement to obtain relaxed lmi conditions new types of fuzzy controller and fuzzy lyapunov function are proposed a salient feature of the lmi conditions derived in this paper is to relate the feasibility of the lmis to the switching speed of each linear subsystem to be exact to the lower bounds of time derivatives of membership functions to illustrate the validity and applicability of the proposed approach two design examples are provided the first example shows that the lmi conditions based on the fuzzy lyapunov function are less conservative than those based on a common standard lyapunov function the second example illustrates the utility of the fuzzy lyapunov function approach in comparison with a piecewise lyapunov function approach

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

a high order accurate difference scheme for complex flow fields a high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented the reason for oscillation production in numerical solutions is analyzed it is caused by a nonuniform group velocity of wavepackets a method of group velocity control for the improvement of the shock resolution is presented in numerical simulation the fifth order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible n s equations a sixth order accurate symmetric compact difference relation is used to approximate the viscous terms and a three stage r k method is used to advance in time in order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets

the projection method for the incompressible navier stokes equations the pressure near a no slip wall an explicit staggered projection method for the incompressible navier stokes equations with no slip walls is analyzed and used in simulations to address several issues related to the pressure boundary condition required when the continuity equation is replaced by the standard pressure poisson equation ppe 2 p u u f first it is shown that a ppe system supplemented with a neumann pressure boundary condition derived from the momentum equation can be made consistent with the navier stokes equations if it is extended with the requirement that 2 u 0 is zero near the wall and the solution is sufficiently smooth this implies that it is possible to formulate a boundary condition for the standard ppe without the necessity to resort to green s functions which is interesting for theoretical reasons second the equivalence is shown between the staggered projection method and the staggered discretization of above ppe system the derivation of the equivalence sheds light upon the so called ppe paradox and leads to an approximation of the wall value of p n which is not required but implied by the staggered projection method third the near wall regularity of a solution of the navier stokes equations is numerically analyzed by means of direct numerical simulation of turbulent channel flow performed with the staggered projection method from the numerical inspection of all terms of the momentum equation in the near wall region it is concluded that the three components of the momentum equation are satisfied on the wall for t 0 for short times but also in the turbulent regime in the limit t 0 the pressure gradient is observed to converge to the initial pressure gradient in the l 2 norm which confirms a disputed theoretical result in literature even in the maximum norm the pressure gradient appears to converge to the initial pressure gradient the only discontinuities observed in the simulations are the discontinuities of the tangential viscous terms and the time derivatives of the tangential velocities on the wall at t 0 thus the numerical results indicate that the regularity of the solution for turbulent channel flow is stronger than claimed by existing theory

on relaxed lmi based designs for fuzzy regulators and fuzzy observers relaxed conditions for stability of nonlinear continuous and discrete time systems given by fuzzy models are presented a theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature numerical results exemplify this fact these results are also used for fuzzy regulators and observers designs the nonlinear systems are represented by fuzzy models proposed by takagi and sugeno 1985 the stability analysis and the design of controllers are described by linear matrix inequalities that can be solved efficiently using convex programming techniques the specification of the decay rate constrains on control input and output are also discussed

robust h control analysis and synthesis for takagi sugeno general uncertain fuzzy systems abstract in this paper robust h control for takagi sugeno general uncertain fuzzy systems where uncertainties come into all the system matrices is considered the main result is to establish equivalent relationships between quadratic stability and quadratic stability with h disturbance attenuation of general uncertain fuzzy systems and h control for fuzzy systems without uncertainty these relationships imply that quadratically stabilizing controllers and quadratically stabilizing controllers with h disturbance attenuation for general uncertain fuzzy systems can be obtained by designing h controllers for fuzzy systems without uncertainties we first give sufficient conditions for the h norm being less than a given number we then consider a general h problem with output feedback controllers and give a design method of h controllers and sufficient conditions which guarantee the required h performance of the closed loop system this design method can be applied to quadratic stabilizing controllers and quadratic stabilizing controllers with h disturbance attenuation for general uncertain fuzzy systems next we analyze quadratic stability and quadratic stability with h disturbance attenuation of general uncertain fuzzy systems and establish equivalent relationships to h control of fuzzy systems without uncertainties based on these relationships we design robust controllers for uncertain fuzzy systems finally examples are given to illustrate the theory

the standard upwind compact difference schemes for incompressible flow simulations compact difference schemes have been used extensively for solving the incompressible navier stokes equations however the earlier formulations of the schemes are of central type called central compact schemes ccs which are dispersive and susceptible to numerical instability to enhance stability of ccs the optimal upwind compact schemes oucs are developed recently by adding high order dissipative terms to ccs in this paper it is found that oucs are essentially not of the upwind type because they do not use upwind biased but central type of stencils furthermore oucs are not the most optimal since orders of accuracy of oucs are at least one order lower than the maximum achievable orders new upwind compact schemes called standard upwind compact schemes sucs are developed in this paper in contrast to oucs sucs are constructed based completely on upwind biased stencils and hence can gain adequate numerical dissipation with no need for introducing optimization calculations furthermore sucs can achieve the maximum achievable orders of accuracy and hence be more compact than oucs more importantly sucs have prominent advantages on combining the stable and high resolution properties which are demonstrated from the global spectral analyses and typical numerical experiments