analysis and design of fuzzy control system abstract a continuous time fuzzy control system which is composed of a fuzzy model and a fuzzy controller is proposed under certain conditions the proposed fuzzy control system can be regarded as a fuzzy pid control system the stability analysis of the fuzzy control system is given a sufficient condition to guarantee the stability of the proposed fuzzy control system is proposed in terms of lyapunov s method the results can be applied to the design of a fuzzy pid control system the design procedure can also be applied to the controller design with a non fuzzy model examples are given to illustrate the design of the proposed fuzzy control system

fredholm volterra integral equation with singular kernel in this paper under certain conditions a series in the legendre polynomials form is used to obtain the solution of fredholm volterra integral equation of the second kind in l 2 1 1 xc 0 t t the uniqueness of the solution is considered the kernel of fredholm integral term is established in a logarithmic form in position while the kernel of volterra integral term is a positive continuous function in time and belongs to the class c 0 t t the solution by series leads us to obtain an infinite system of linear algebraic equations where the convergence of this system is studied in the end of this paper the fredholm volterra integral equation of the first kind is established and its solution is discussed

robust h sub spl infin control for uncertain discrete time delay fuzzy systems via output feedback controllers this work investigates the problem of robust output feedback h sub spl infin control for a class of uncertain discrete time fuzzy systems with time delays the state space takagi sugeno fuzzy model with time delays and norm bounded parameter uncertainties is adopted the purpose is the design of a full order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h sub spl infin norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities lmis a sufficient condition for the solvability of this problem is presented explicit expressions of a desired output feedback controller are proposed when the given lmis are feasible the effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust h sub spl infin control for a class of uncertain nonlinear discrete delay systems

a correlated fracture network modeling and percolation properties 1 we present a model of fractures based on the idea that the elastic free energy due to the fracture density follows a boltzmann distribution the resulting expression for the spatial correlation in the displacement of fractures is used as an objective function in a simulated annealing algorithm to generate realizations of correlated fracture networks this approach determines the appropriate statistical distribution for the fractures e g length distribution rather than imposing them as is done conventionally the model consists of two families of parallel fractures which are perpendicular under isotropic conditions there also exists a positive correlation between the position of fractures and their lengths that is large fractures have their neighbors located at greater distance than small fractures finally we use the realizations of correlated fracture networks in the basic methodology of the percolation approach and investigate the model percolation properties in particular the scaling exponents of the connectivity are found to be different from the conventional uncorrelated values

robust h sub spl infin control for fuzzy systems with frobenius norm bounded uncertainties in this paper we investigate the problem of robust h sub spl infin performance and stabilization for a class of uncertain fuzzy systems with frobenius norm bounded parameter uncertainties in all system matrices both continuous and discrete time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems unlike the bounded real lemma in the linear theory of robust h sub spl infin control where necessary and sufficient conditions were obtained only sufficient condition based on lyapunov method is shown furthermore connection between robust h sub spl infin problems involving uncertainty and standard uncertainty free h sub spl infin problems is established via matrix algebra as for controller synthesis a state feedback fuzzy control law is designed via relaxed linear matrix inequality lmi formulations

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

fredholm volterra integral equation in contact problem in this work the solution of the integral equation of the mixed type in the domain w x y z email protected

fuzzy systems and controllers lyapunov tools for a regionwise approach this paper reviews a class of tools which can help to check the stability of fuzzy linguistic controllers which is a difficult task due to their regionwise structure the application of conventional methods when considering a fuzzy controller as a global nonlinear controller often leads to conservative stability results the use of appropriate continuous or piecewise continuous lyapunov functions allows to address the stability of nonlinear systems under fuzzy control while taking into account the local structure of the fuzzy controllers some methods are presented which enforce the global lyapunov function to decrease when leaving one subspace for another closer to the equilibrium using concentric domains and providing less conservative conditions

numerical solution of integral equations 1 a survey of boundary integral equation methods for the numerical solution of laplace s equation in three dimensions 2 superconvergence 3 perturbed projection methods for various classes of operator and integral equations 4 numerical solution of parallel processors of two point boundary value problems of astrodynamics 5 introduction to the numerical solution of cauchy singular integral equations 6 convergence theorems for singular integral equations 7 planing surfaces 8 abel integral equations

on dynamic problem and integral equation in this work the fredholm integral equation of the second kind with logarithmic kernel is established from dynamic elastic problem such problem appears for example when a stamp of length 2a is impressed into the boundary of a strip y h by a variable force p t with time t 0 t t also the strip without fraction lies on a rigid elastic layer of thickness h the solution of the integral equation is obtained using chebyshev polynomial a numerical result is obtained for the problem

a fast algorithm for solving the generalized airfoil equation abstract the present paper is devoted to the quadrature method for cauchy type singular integral equations on 1 1 with an additional logarithmic singularity of the kernel an algorithm being based on this method is given whose realization only requires a computational work of o n ln n operations in order to determine n unknown coefficients of the approximate solution furthermore in a scale of weighted sobolev like spaces on 1 1 having analogous properties like the classical sobolev spaces on the unit circle the order of convergence is optimal

solving boundary value problems integral and integro differential equations using gegenbauer integration matrices we introduce a hybrid gegenbauer ultraspherical integration method hgim for solving boundary value problems bvps integral and integro differential equations the proposed approach recasts the original problems into their integral formulations which are then discretized into linear systems of algebraic equations using gegenbauer integration matrices gims the resulting linear systems are well conditioned and can be easily solved using standard linear system solvers a study on the error bounds of the proposed method is presented and the spectral convergence is proven for two point bvps tpbvps comparisons with other competitive methods in the recent literature are included the proposed method results in an efficient algorithm and spectral accuracy is verified using eight test examples addressing the aforementioned classes of problems the proposed method can be applied on a broad range of mathematical problems while producing highly accurate results the developed numerical scheme provides a viable alternative to other solution methods when high order approximations are required using only a relatively small number of solution nodes

robust quadratic optimal control of ts fuzzy model based dynamic systems with both elemental parametric uncertainties and norm bounded approximation error this paper considers the design problem of the robust quadratic optimal parallel distributed compensation pdc controllers for takagi sugeno ts fuzzy model based control systems with both elemental parametric uncertainties and norm bounded approximation error by complementarily fusing the robust stabilizability condition the orthogonal functions approach ofa and the hybrid taguchi genetic algorithm htga an integrative method is presented in this paper to design the robust quadratic optimal pdc controllers such that 1 the uncertain ts fuzzy model based control systems can be robustly stabilized and 2 a quadratic integral performance index for the nominal ts fuzzy model based control systems can be minimized in this paper the robust stabilizability condition is proposed in terms of linear matrix inequalities lmis by using the ofa and the lmi based robust stabilizability condition the robust quadratic optimal pdc control problem for the uncertain ts fuzzy model based dynamic systems is transformed into a static constrained optimization problem represented by the algebraic equations with constraint of lmi based robust stabilizability condition thus greatly simplifying the robust optimal pdc control design problem then for the static constrained optimization problem the htga is employed to find the robust quadratic optimal pdc controllers of the uncertain ts fuzzy model based control systems two design examples of the robust quadratic optimal pdc controllers for an uncertain inverted pendulum system and an uncertain nonlinear mass spring damper mechanical system are given to demonstrate the applicability of the proposed integrative approach

fredholm integral equation with potential kernel and its structure resolvent the purpose of this paper is to establish and solve the fredholm integral equation of the second kind with potential kernel from the semi symmetric hertz problem for two different elastic materials in three dimensions the kernel of the problem is represented in the non homogeneous wave equation also the structure resolvent of the problem is obtained

the perturbed galerkin method for cauchy singular integral equations with constant coefficients we have considered the numerical solution of cauchy singular integral equations with constant coefficients via a polynomial based galerkin method l 2 and uniform convergence results are proved under holder continuity conditions on the kernel and right hand side and taking into account the quadrature errors produced when inner products are replaced by numerical quadratures these results generalize those of miel who considered only the case of equations of the first kind with index 0

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

simulating the dynamics of flexible bodies and vortex sheets we present a numerical method for the dynamics of a flexible body in an inviscid flow with a free vortex sheet the formulation is implicit with respect to body variables and explicit with respect to the free vortex sheet we apply the method to a flexible foil driven periodically in a steady stream we give numerical evidence that the method is stable and accurate for a relatively small computational cost a continuous form of the vortex sheet regularization permits continuity of the flow across the body s trailing edge nonlinear behavior arises gradually with respect to driving amplitude and is attributed to the rolling up of the vortex sheet flow quantities move across the body in traveling waves and show large gradients at the body edges we find that in the small amplitude regime the phase difference between heaving and pitching which maximizes trailing edge deflection also maximizes power output the phase difference which minimizes trailing edge deflection maximizes efficiency

on the solution of linear and nonlinear integral equation the purpose of this paper is to establish the solution of fredholm volterra integral equation of the second kind in the space l 2 w xc 0 t considering the following when fredholm integral term in li 2 w and volterra integral term in 0 t are linear also each of fredholm or volterra integral term is linear while the other term is nonlinear here w is defined as the domain of integration with respect to position while t is consider as the time email protected 0 t t also the fredholm volterra integral equation of the first kind is established as special case of these work many special in one two and three dimensional problems of integral equation are considered representing the kernel of fredholm integral term in the form of logarithmic function carleman function potential and generalized potential function and macdonald function are considered

robust stability of uncertain discrete time singular fuzzy systems this paper considers the problem of robust stability analysis of uncertain discrete time singular fuzzy systems described by a class of extended takagi sugeno fuzzy dynamic models with time varying norm bounded parameter uncertainties a sufficient condition ensuring a discrete singular fuzzy system to be regular causal and stable is proposed in terms of a set of linear matrix inequalities based on this a robust stability condition is obtained both of these conditions can be checked by using recently developed algorithms in solving lmis examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions

airfoil polynomials for solving integro differential equations with logarithmic kernel abstract in this paper we introduce a collocation method for approximate solution of an integro differential equations with logarithmic kernel using airfoil polynomials we prove the existence of the solution for the approximate equation and we perform the error analysis a system of linear equations is to be solved finally some numerical examples illustrate the accuracy of the method

new error estimates for galerkin method to an airfoil equation in this paper we consider new error estimates under the weighted chebyshev norm for galerkin method to an airfoil equation galerkin discretisation is discussed the smoothness conditions of the input functions are improved i e they need to be holder continuous with 12 m 1

integral equation of mixed type and integrals of orthogonal polynomials a method is used to obtain the general solution of the fredholm volterra integral equation of the first kind fviefk in the space l2 0 a c 0 t 0 x a 0 t t the kernel of the fredholm integal term is considered in a generalized discontinuous form which belongs to c 0 a 0 a while the kernel of volterra integral term is a positive continuous function in the class c 0 t many interesting cases of integrals of orthogonal polynomials and spectral relationships are obtained and established from this work

bernoulli polynomials for the numerical solution of some classes of linear and nonlinear integral equations a new operational matrix for integration of bernoulli polynomials is introduced by using this new operational matrix of integration and the so called collocation method linear volterra and nonlinear volterra fredholm hammerstein integral equations are reduced to systems of algebraic equations with unknown bernoulli coefficients some error estimations are provided and illustrative examples are also included to demonstrate the efficiency and applicability of the technique a new operational matrix for integration of bernoulli polynomials is introduced a collocation method is used to reduce equations to systems of algebraic equations some error bounds and convergence results are provided for the proposed method the efficiency and applicability of the technique are checked by some examples

a fast chebyshev method for simulating flexible wing propulsion abstract we develop a highly efficient numerical method to simulate small amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid we allow the wing s elastic modulus and mass density to vary arbitrarily with an eye towards optimizing these distributions for propulsive performance the method to determine the wing kinematics is based on chebyshev collocation of the 1d beam equation as coupled to the surrounding 2d fluid flow through small amplitude analysis of the euler equations with trailing edge vortex shedding the complete hydrodynamics can be represented by a nonlocal operator that acts on the 1d wing kinematics a class of semi analytical solutions permits fast evaluation of this operator with o n log n operations where n is the number of collocation points on the wing this is in contrast to the minimum o n 2 cost of a direct 2d fluid solver the coupled wing fluid problem is thus recast as a pde with nonlocal operator which we solve using a preconditioned iterative method these techniques yield a solver of near optimal complexity o n log n allowing one to rapidly search the infinite dimensional parameter space of all possible material distributions and even perform optimization over this space

on the weighted galerkin method of numerical solution of cauchy type singular integral equations the well known weighted galerkin method for the direct numerical solution of cauchy type singular integral equations of the first and the second kind based on the approximation of the unknown function by a finite series of appropriate orthogonal polynomials is shown to be identical to the corresponding method based on the reduction of the cauchy type singular integral equation to an equivalent fredholm integral equation of the second kind and the application to the latter of the weighted galerkin method this result permits the direct transfer of the whole set of convergence and rate of convergence results for the weighted galerkin method of numerical solution of fredholm integral equations with regular kernels to the case of cauchy type singular integral equations an application to the case where chebyshev polynomials are used is also made and the available convergence results for the direct weighted galerkin method are rederived with essentially no analysis

a new approach to robust and non fragile h control for uncertain fuzzy systems this paper investigates the robust h control and non fragile control problems for takagi sugeno t s fuzzy systems with linear fractional parametric uncertainties the robust h control problem is to design a state feedback controller such that the robust stability and a prescribed h performance of the resulting closed loop system is ensured and the non fragile h control problem is to design a state feedback controller with parameter uncertainties based on the linear matrix inequality lmi approach new sufficient conditions for the solvability of the two problems are obtained it is shown that the desired state feedback fuzzy controller can be constructed by solving a set of lmis numerical examples are also provided to demonstrate the effectiveness of the proposed design method

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

generation of long range correlations in large systems as an optimization problem we propose an efficient method of generating long range correlations in large systems the development of this method was motivated by the problem of constructing an optimal model for a large scale porous medium there are typically long range correlations in the properties of such porous media such as their permeability and porosity for which there are usually only limited data the optimal model must not only honor preserve the available data and their correlation function but also accurately predict the future behavior of fluid flow in the media we formulate the problem of generating the long range correlations as one of optimization and utilize simulated annealing to generate a d dimensional array which contains the correlations and honors the existing data the optimization process is based on the data s correlation function the method is therefore free of the many numerical difficulties and or limitations that most previous techniques suffer from it is completely general and may be used for generating long range correlations with any type of correlation function in both isotropic and anisotropic media representative examples are presented and the method s efficiency and accuracy are discussed

discrete projection methods for cauchy singular integral equations with constant coefficients we consider proving the mean square and uniform convergence of various discrete galerkin and collocation methods for cauchy singular integral equations with constant coefficients for galerkin s method the convergence rates improve those given in an earlier paper while for collocation methods the results appear to be new in particular we consider product quadrature methods for equations with discontinuous coefficients and develop and prove the convergence of a new algorithm for equations of the first kind with index zero and logarithmically singular kernels

fredholm volterra integral equation of the first kind and contact problem regular and singular asymptotic methods are applied to one and two dimensional fredholm volterra integral equation f vie of the first kind that arise in the treatment of various two dimensional axisymmetric and three dimensional problems with mixed boundary conditions in the mechanics of continuous media the solution of the integral equation is obtained in the space l 2 w xc 0 t 0

further convergence results for the weighted galerkin method of numerical solution of cauchy type singular integral equations the convergence of the weighted lalerkin method based on chcbvshen or jacobi polvnoinials for the direct numerical solution of one dimensional real cauchv tvpe singular integral equations of the first and of the second kind on a finite interval is proved under sufficientlv weak continuitv assumptions for the kernels and the right side functions of thc integral equations

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

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

numerical solution of fredholm volterra integral equation in one dimension with time dependent in this paper we consider fredholm volterra integral equation in one dimension with time dependent the kernel of the fredholm term is assumed to be singular while the kernel of volterra term is continuous the existence of the solution is proved and a numerical method is presented to get an approximate to such solution

connectivity of random fault networks following a power law fault length distribution we present a theoretical and numerical study of the connectivity of fault networks following power law fault length distributions n l l a as expected for natural fault networks different regimes of connectivity are identified depending on a for a 3 faults smaller than the system size rule the network connectivity and classical laws of percolation theory apply on the opposite for a 1 the connectivity is ruled by the largest fault in the system for 1 a 3 both small and large faults control the connectivity in a ratio which depends on a the geometrical properties of the fault network and of its connected parts density scaling properties are established at the percolation threshold finally implications are discussed in the case of fault networks with constant density in particular we predict the existence of a critical scale at which fault networks are always connected whatever a smaller than 3 and whatever their fault density

vortex design problem in this investigation we propose a computational approach for the solution of optimal control problems for vortex systems with compactly supported vorticity the problem is formulated as a pde constrained optimization in which the solutions are found using a gradient based descent method recognizing such euler flows as free boundary problems the proposed approach relies on shape differentiation combined with adjoint analysis to determine cost functional gradients in explicit tracking of interfaces vortex boundaries this method offers an alternative to grid based techniques such as the level set methods and represents a natural optimization formulation for vortex problems computed using the contour dynamics technique we develop and validate this approach using the design of 2d equilibrium euler flows with finite area vortices as a model problem it is also discussed how the proposed methodology can be applied to euler flows featuring other vorticity distributions such as vortex sheets and to time dependent phenomena

polynomially based multi projection methods for fredholm integral equations of the second kind in this paper we propose a multi projection and iterated multi projection methods for fredholm integral equations of the second kind with a smooth kernel using polynomial bases we obtain super convergence rates for the approximate solutions more precisely we prove that in m galerkin and m collocation methods not only iterative solution u n approximates the exact solution u in the supremum norm with the order of convergence n 4 k but also the derivatives of u n approximate the corresponding derivatives of u in the supremum norm with the same order of convergence n being the degree of polynomial approximation and k being the smoothness of the kernel

discrete product integration methods for eigen problems of a class of non compact integral operators in this paper we develop discrete product integration methods for the eigenvalue problem of certain kind of non compact linear operators given as the sum of a multiplication and a weakly singular integral operator our discrete product integration scheme is a product integration scheme in which the weakly singular integrals appeared in the weight functions are computed numerically by gauss legendre type quadrature formulas we show that our methods are convergent and their convergence rates are max h r 1 m 2 d which is dependent on the accuracy of both the numerical quadrature and approximate solution of the product integration scheme our numerical results confirm that discrete product integration methods are particularly efficient for solving this kind eigenvalue problem

a fast solver for the hilbert type singular integral equations based on the direct fourier spectral method abstract in this paper we develop a fast and direct fourier spectral method for solving the hilbert type singular integral equation this method leads to a fully discrete linear system whose coefficient matrix is expressed as the sum of a sparse matrix and a quasi circulant matrix we show that it requires a nearly linear computational cost to obtain and then solve the fully discrete linear system we also prove that the proposed algorithm preserves the optimal convergent order one numerical experiment is presented to demonstrate its approximate accuracy and computational efficiency verifying the theoretical estimates

delay dependent robust hbox it h _ infty control for uncertain discrete time fuzzy systems with time varying delays this paper deals with the robust h infin control problem for discrete time takagi sugeno t s fuzzy systems with norm bounded parametric uncertainties and interval time varying delays first based on a new lyapunov functional we present a sufficient condition guaranteeing that the resulting closed loop system is robustly stable and satisfies a prescribed h infin performance level the lyapunov functional used here depends on not only the fuzzy basis function but on the lower and upper bounds of the time varying delay as well second two classes of delay dependent conditions for the existence of the concerned h infin fuzzy controllers are given in terms of relaxed linear matrix inequalities lmis and a desired controller can be designed by using the solutions to these lmis finally a numerical example is provided to demonstrate the effectiveness of the proposed design method

the approximate solution of a class of fredholm integral equations with a weakly singular kernel a method for finding the numerical solution of a weakly singular fredholm integral equation of the second kind is presented the taylor series is used to remove singularity and legendre polynomials are used as a basis furthermore the legendre function of the second kind is used to remove singularity in the cauchy type integral equation the integrals that appear in this method are computed in terms of gamma and beta functions and some of these integrals are computed in the cauchy principal value sense without using numerical quadratures four examples are given to show the accuracy of the method

stabilization for t s model based uncertain stochastic systems this paper considers the stabilization problem of a class of uncertain ito stochastic fuzzy systems driven by a multidimensional wiener process the uncertainty modeled in the systems is of the linear fractional type which includes the norm bounded uncertainty as a special case the objective is to design a state feedback fuzzy controller such that the closed loop system is robustly asymptotically stable under a stochastic setting by using a stochastic lyapunov approach sufficiency conditions for the stability and stabilization of this class of systems are established based on a novel matrix decomposition technique the derived stability conditions are then employed to design controllers which stabilize the uncertain ito stochastic fuzzy systems two simulation examples are given to illustrate the effectiveness of the approaches proposed

a numerical method and efficient preconditioner for generalized airfoil equations in this paper the generalized airfoil equations with cauchy algebraic singularity are researched by introducing the collocation method to conquer the singularity of the integral equation theoretical analysis and examples showed this method has accuracy o h m 1 with m the order of the interpolate polynomial in addition by separating the singular part into two so that they can offset against each other in the collocation points a new equivalent integrate function is also constructed moreover to accelerate the convergence of solving the obtained linear system a tridiagonal preconditioner is also presented for the singular integral operator by the operator splitting idea compared to the traditional tridiagonal preconditioner our method is more easily computed by an explicit inverse finally some numerical examples are presented to illustrate the behavior of the collocation method and this preconditioner

regularizing a vortex sheet near a separation point current methods for computing vortex sheet separation use a regularization parameter which is discontinuous from the body to the vortex sheet we propose two methods for reducing the errors associated with the discontinuity and improving convergence with respect to the regularization parameter the velocity smoothing method is the simpler of the two and removes the discontinuity in regularization from one of the two equations where it occurs the tapered smoothing method removes the discontinuity from both equations in a model problem both methods are found to converge much more rapidly with exponents 3 2 and 2 versus 1 2 for the standard method as the regularization parameter tends to zero unsteady algorithms are proposed for evolving the free sheet using the two methods and are tested in a benchmark problem accuracy is significantly improved for similar computational expense

optimal convergence rates for some discrete projection methods using recent results of sloan on hyperinterpolation operators j approx theory 81 1995 238 we show how to obtain optimal convergence rates for a variety of discrete polynomially based galerkin and collocation methods for a variety of fredholm and singular integral equations these results improve on those given in golberg j integral equations appl 8 1996 307 and are analogous to those obtained by atkinson and bogomolny for spline based methods math comp 48 1987 596 these results are then applied to analyze double approximation methods where both numerical integration and data errors are considered here we show that the errors are dominated by those in the data hence it may not be possible in practice to obtain optimal convergence rates unless the data can be computed exactly

robust h control for uncertain fuzzy systems with distributed delays via output feedback controllers this paper investigates the problem of robust h output feedback control for a class of uncertain fuzzy systems with distributed delays the system is described by a state space takagi sugeno fuzzy model with distributed delays and norm bounded parameter uncertainties the aim is to design a fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed loop system and guarantees an h norm bound constraint on disturbance attenuation for all admissible uncertainties in terms of linear matrix inequalities a sufficient condition for the solvability of this problem is presented finally simulation examples are provided to illustrate the effectiveness of the proposed design approach

numerical calculations of critical densities for lines and planes critical percolation densities have been calculated numerically for large systems of lines in two dimensions and planes in three dimensions results for lines of varying length have been successfully predicted from the constant length case in special cases very large systems of up to 1 4 million lines have been studied by calculating critical densities for a range of system sizes and using a finite size scaling argument a prediction of the infinite critical density is made for the two dimensional system with fixed length orthogonal lines this corresponds to 3 11 intersections per line for the three dimensional system of fixed size orthogonal planes the prediction is 2 00 intersections per plane

on a method for solving an integral equation in the displacement contact problem in this paper the solution in a series form of the integral equation of the mixed type in the space l w xc 0 t is obtained where w x y z

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

the galerkin method for singular integral equations revisited abstract in an earlier work the author has obtained error bounds for the galerkin method for solving cauchy singular integral equations discovering that the usually neglected constants contain the riemann zeta function when evaluated in the supremum norm the aim of this investigation is twofold to show that the occurrence of the riemann zeta function in the error bound for the chebyshev norm is sharp and secondly to use this result to obtain a class of forcing functions for which the method does not yield an approximate solution differing from the analytical one by at most a prescribed error tolerance these counterexamples indicate that in practical situations for functions exhibiting a behavior similar to the one presented here galerkin s method might not lead to an acceptable solution

a descriptor system approach to non fragile h control for uncertain fuzzy neutral systems in this paper the problem of non fragile h control for a class of uncertain takagi sugeno t s fuzzy neutral systems with linear fractional parametric uncertainties is considered the non fragile h control problem is to design a state feedback controller with parameter uncertainties such that the l 2 induced gain of the mapping from the exogenous input to the controlled output is less than some prescribed level based on lyapunov krasovskii functional the descriptor model transformation and lmi approach new sufficient conditions for solvability of this problem are obtained it is shown that by a novel controller design method the desired state feedback fuzzy controller can be constructed by solving a set of lmis and the minimum h disturbance attenuation level can be obtained via using the lmi algorithm mincx finally an illustrative numerical example is provided to demonstrate correctness and effectiveness of the theoretical results

a robust multi objective dpdc for uncertain t s fuzzy systems this paper offers a design procedure for a robust pole placement problem with h objective via dynamic output feedback control for a class of uncertain fuzzy systems takagi sugeno t s fuzzy system is used for modeling and dynamic parallel distributed compensation dpdc technique is employed in the controller design solutions to the problems are derived in terms of a family of linear matrix inequalities lmis and uncertainties are directly considered in the conditions that determine the controller effectiveness of the proposed design technique is illustrated by simulation for an inverted pendulum system

on the numerical solutions of fredholm volterra integral equation toeplitz matrix method and the product nystrom method are described for mixed fredholm volterra singular integral equation of the second kind the results are compared with the exact solution of the integral equation the error of each method is calculated

connectivity of fracture systems a percolation theory approach critical percolation densities have been found numerically for various systems of lines uniformly distributed in the plane the average number of intersections per line at percolation has also been found and varies only slightly over the cases considered it may therefore provide a useful rule of thumb for deciding whether a system percolates an estimate of the critical percolation density from the lattice percolation probability is presented possible extensions of the techniques described to three dimensions are discussed

a note on solving cauchy integral equations of the second kind by projection the purpose of this paper is to approximate the solution of a cauchy integral equation of the second kind using projection finite rank approximations and a regularization procedure we us the kantorovich projection the sloan projection the galerkin projection respectively we give a general framework and we prove the existence of the solution for a projection schemes

a note on solving cauchy integral equations of the first kind by iterations abstract the successive approximation method was applied for the first time by n i ioakimidis to solve practical cases of a cauchy singular integral equation the airfoil one in this paper we study a more general case we prove the convergence of the method in this general case the proposed method has been tested for two kernels which are particularly important in practice finally some numerical examples illustrate the accuracy of the method

time optimal control of t s fuzzy models via lie algebra this paper investigates a geometric property of time optimal problem in the takagi sugeno t s fuzzy model via lie algebra we will focus on the existence of a time optimal solution singularity of switching function and number of switching these inherent problems are considered because of their rich geometric properties the sufficient condition for the existence of a time optimal solution reveals the controllability of t s fuzzy model that can be found by the generalized rank condition the time optimal controller can be found as the bang bang type with a finite number of switching by applying the maximum principle in the study of the singularity problem we will focus on the switching function whenever it vanishes over a finite time interval finally we show that the bounded number of switching can be found if the t s model also a nonlinear system is solvable

connectivity properties of two dimensional fracture networks with stochastic fractal correlation 1 we present a theoretical and numerical study of the connectivity of fracture networks with fractal correlations in addition to length distribution this spatial property observed on most fracture networks conveys long range correlation that may be crucial on network connectivity we especially focus on the model that comes out relevant to natural fracture network a fractal density distribution for the fracture centers dimension d and a power law distribution for the fracture lengths exponent a n l l a three different regimes of connectivity are identified depending on d and on a for a d 1 the connectivity is ruled by fractures much smaller than the system size with a strong control of spatial correlation the connectivity now decreases with system scale finally for the self similar case a d 1 which corresponds to the transition between the two previous regimes connectivity properties are scale invariant percolation threshold corresponds to a critical fractal density and the average number of intersections per fracture at threshold is a scale invariant as well

galerkin s method for operator equations with nonnegative index with application to cauchy singular integral equations abstract we consider solving operator equation 1 hu ku f where h and k are bounded linear operators between two real hilbert spaces h1 and h2 operator h is assumed to have a finite dimensional nullspace n h and a bounded right inverse h1 h2 h1 and k is compact it follows that dim n h k dim n h so that to obtain uniqueness the m additional conditions 2 u k 1 bk k 1 2 h dim n h m are imposed where the k k 1m are an orthonormal basis for n h to solve 1 and 2 these equations are converted to an equivalent equation of the second kind to which galerkin s method is applied using the basis 1 2 m m 1 n it was shown that this method is equivalent to the method of weighted residuals when h 1 h the adjoint of h the results are applied to obtain convergence proofs of some numerical methods for solving several classes of cauchy singular integral equations whose kernels are only square integrable

galerkin solution of a singular integral equation with constant coefficients galerkin methods are used to approximate the singular integral equation email protected x email protected 1 email protected t email protected 1 1k t x f t dt f x 10 are constants in this case f is decomposed as f x 1 x a 1 x bu x where email protected 0 0 is a small enough constant

a note on the sparse representation of discrete integral operators we show how to give sparse matrix representations for a number of integral operators in one and two dimensions typically this results when using a galerkin or a discrete galerkin method related collocation methods using the same basis do not yield sparse representations this suggests that the traditional preference of collocation over galerkin methods be re examined in light of exploiting sparseness in a number of known algorithms

a semi infinite crack in front of a circular thermally mismatched heterogeneity abstract the stress intensity factors sifs of a semi infinite crack in front of a thermally and elastically mismatched circular heterogeneity are studied based on a singular integral equation technique and on a self consistent method it is shown that the solution resulting from the self consistent method is equivalent to the one from the cauchy type singular integral equation if the kernel function in the integral equation is completely ignored the self consistent solution is then compared with the numerical solution of the integral equation for the full range of elastic mismatch using various discretization techniques for dundurs parameters within the range 0 6 and 4 the the sifs predicted by the self consistent formula agree within 7 or better when compared with the numerical results provided that the crack tip is not situated extremely close to the heterogeneity finally it is analyzed how the convergence of the sifs of crack tips which are extremely close to the heterogeneity is influenced by the choice of discretization scheme to generate computer codes which are easy to implement time efficient and numerically accurate it is advantageous to use techniques which operate on a finite interval 1 1 i e gauss chebyshev lobatto chebyshev as compared with those which cover the positive x axis 0 i e radau chebyshev or gausshermite consequently it is advisable to map the semi infinite crack into a crack of finite size by using suitable transforms it will be shown that among the discretizations for a finite interval the fastest to converge are those which explicitly use the end points 1 and 1 lobatto chebyshev followed closely by polynomial extrapolation of discrete solution data for 1 1 into the crack tips

an algebraic approach to robust h control via state feedback abstract this paper considers the problem of robust h control design for linear uncertain systems we show that for a certain type of time varying norm bounded parameter uncertainty the problem is equivalent to an h control problem therefore a complete solution is achieved by using the existing results of h control theory the paper presents a state feedback design which stabilizes the plant for all admissible uncertainties and also guarantees a prescribed level of disturbance attenuation in a certain sense

numerical solution of stochastic linear heat conduction problem by using new algorithms we consider a stochastic linear heat conduction problem so it is reduced to a special integral equation of the second kind our aim in this paper is to give stable numerical algorithms for approximating solution of integral equation and heat conduction

h _ infty fuzzy observer based control for a class of nonlinear distributed parameter systems with control constraints an hinfin fuzzy observer based control design is proposed for a class of nonlinear parabolic partial differential equation pde systems with control constraints for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement in the proposed control scheme galerkin s method is initially applied to the pde system to derive a nonlinear ordinary differential equation ode system that accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a fuzzy observer based controller is developed to stabilize the nonlinear pde system and achieve an optimized hinfin disturbance attenuation performance for the finite dimensional slow system while control constraints are respected the outcome of the hinfin fuzzy observer based control problem is formulated as a bilinear matrix inequality bmi optimization problem a local optimization algorithm that treats the bmi as a double linear matrix inequality is presented to solve this bmi optimization problem finally the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness

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

dependency of percolation critical exponents on the exponent of power law size distribution abstract the standard percolation theory uses objects of the same size moreover it has long been observed that the percolation properties of the systems with a finite distribution of sizes are controlled by an effective size and consequently the universality of the percolation theory is still valid in this study the effect of power law size distribution on the critical exponents of the percolation theory of the two dimensional models is investigated two different object shapes i e stick shaped and square are considered these two shapes are the representative of the fractures in fracture reservoirs and the sandbodies in clastic reservoirs the finite size scaling arguments are used for the connectivity to determine the dependency of the critical exponents on the power law exponent in particular the deviations of percolation exponents from their universal values as well as the connectivity behavior of such systems are investigated numerically as a result this extends the applicability of the conventional percolation approach to study the connectivity of systems with a very broad size distribution

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

robust stability of impulsive takagi sugeno fuzzy systems with parametric uncertainties this paper presents a kind of time varying impulsive takagi sugeno t s fuzzy model with parametric uncertainties in which each subsystem of the model is time varying several robust stabilities of time varying systems with parametric uncertainties such as general robust stability robustly asymptotical stability and exponential stability are studied using uniformly positive definite matrix functions and the lyapunov method specifically robust stability conditions of time invariant impulsive t s fuzzy systems are also derived in the formulation of quasi linear matrix inequalities qlmis and an iterative lmis algorithm is designed for solving qlmis finally a unified chaotic system with continuous periodic switch and a unified time invariant chaotic system are used for demonstrating the effectiveness of our respective results

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

numerical solution for system of cauchy type singular integral equations with its error analysis in complex plane abstract in this paper the problem of finding numerical solution for a system of cauchy type singular integral equations of first kind with index zero is considered the analytic solution of such system is known but it is of limited use as it is a nontrivial task to use it practically due to the presence of singularity in the known solution itself therefore a residual based galerkin method is proposed with legendre polynomials as basis functions to find its numerical solution the proposed method converts the system of cauchy type singular integral equations into a system of linear algebraic equations which can be solved easily further hadamard conditions of well posedness are established for system of cauchy singular integral equations as well as for system of linear algebraic equations which is obtained as a result of approximation of system of singular integral equations with cauchy kernel the theoretical error bound is derived which can be used to obtain any desired accuracy in the approximate solution of system of cauchy singular integral equations the derived theoretical error bound is also validated with the help of numerical examples

robust h nonlinear modeling and control via uncertain fuzzy systems in theory an algebraic riccati equation are scheme applicable to robust h quadratic stabilization problems of a class of uncertain fuzzy systems representing a nonlinear control system is investigated it is proved that existence of a set of solvable ares suffices to guarantee the quadratic stabilization of an uncertain fuzzy system while satisfying h norm bound constraint it is also shown that a stabilizing control law is reminiscent of an optimal control law found in linear quadratic regulator and a linear control law can be immediately discerned from the stabilizing one in practice the minimal solution to a set of parameter dependent ares is somewhat stringent and instead a linear matrix inequalities formulation is suggested to search for a feasible solution to the associated ares the proposed method is compared with the existing fuzzy literature from various aspects

robust fuzzy h control for uncertain nonlinear systems via state feedback an lmi approach this paper presents a method for designing robust fuzzy h controllers which stabilize nonlinear systems and guarantee an induced l2 norm bound constraint on disturbance attenuation for all admissible uncertainties takagi and sugeno fuzzy models with uncertainties are used as the model for the uncertain nonlinear systems fuzzy control systems utilize the concept of the so called parallel distributed compensation pdc using a single quadratic lyapunov function the stability with decay rate and disturbance attenuation for takagi and sugeno fuzzy model with parameter uncertainties are discussed a sufficient condition for the presence of the robust fuzzy h controllers is then presented in terms of linear matrix inequalities lmis finally design examples of robust fuzzy h controllers for uncertain nonlinear systems are presented

h2 guaranteed cost fuzzy control for uncertain nonlinear systems via linear matrix inequalities abstract this paper deals with h2 guaranteed cost gc fuzzy control problem for uncertain continuous time nonlinear systems the state feedback case and observer based output feedback case are considered the takagi and sugeno t s fuzzy model is employed to represent a nonlinear system with parametric uncertainties sufficient conditions for the existence of h2 gc fuzzy controllers are given in terms of linear matrix inequalities lmis the suboptimal h2 gc fuzzy controllers are given by means of the lmi optimization procedures which cannot only guarantee that the closed loop overall fuzzy systems are globally asymptotically stable but also provide an optimized upper bound on the quadratic performance cost finally an example is presented to illustrate the effectiveness of the proposed fuzzy controllers

numerical solution of integral equations with logarithmic cauchy and hadamard type singularities this study presents an extension of the piecewise quadratic polynomial technique to solve singular integral equations with logarithmic and hadamard type singularities for completeness and continuity the evaluation of the weights for logarithmic cauchy and hadamard type singularities are given explicitly numerical results concerning logarithmic and hadamard type singular integral equations are compared with the known solutions the solution of cauchy type singular integral equations was discussed in detail in a previous study by miller and keer 1998 john wiley sons ltd

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

numerical treatment of solving singular integral equations by using sinc approximations abstract in this paper we propose numerical treatment for singular integral equations the methods are developed by means of the sinc approximation with smoothing transformations such approximation is an effective technique against the singularities of the equations and achieves exponential convergence therefore the methods improve conventional results where only polynomial convergence have been reported the resulting algebraic system is solved by least squares approximation and leap frog algorithm estimation of errors of the approximate solution is presented some experimental tests are presented to show the efficient of the proposed methods

the use of piecewise quadratic polynomials for the solution of singular integral equations of cauchy type abstract a method for the numerical solution of singular integral equations of cauchy type is developed the unknown function is expressed as a product of a weight function and a continuous function t the continuous function t is approximated by piecewise quadratic polynomials and the singular integral equation is reduced to a linear algebraic system numerical examples are given and comparisons are made with the widely used gauss type methods