an a posteriori parameter choice for tikhonov regularization in hilbert scales leading to optimal convergence rates an a posteriori parameter choice for tikhonov regularization in hilbert scales is proposed that leads to optimal convergence rates the advantage of this method is that knowledge of the smoothness parameters of both the operator and the exact solution is not needed the finite dimensional realization of this method is also discussed numerical examples confirm the theoretical results

robust stabilization of nonlinear multiple time delay large scale systems via decentralized fuzzy control to overcome the effect of modeling errors between nonlinear multiple time delay subsystems and takagi sugeno t s fuzzy models with multiple time delays a robustness design of fuzzy control is proposed in this work in terms of lyapunov s direct method a delay dependent stability criterion is hence derived to guarantee the asymptotic stability of nonlinear multiple time delay large scale systems based on this criterion and the decentralized control scheme a set of model based fuzzy controllers is then synthesized via the technique of parallel distributed compensation pdc to stabilize the nonlinear multiple time delay large scale system finally a numerical example with simulations is given to demonstrate the concepts discussed throughout this work

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

robust h control of uncertain fuzzy systems under time varying sampling robust h sampled data control for uncertain fuzzy systems is discussed in many practical situations a system is modeled as a continuous time fuzzy system while the control input is the zero order hold which can be represented as a piecewise continuous delay here we take a delay system approach to the h sampled data control problem the closed loop system with a sampled data state feedback controller becomes a system with time varying delay first h performance conditions for the closed loop system are given in terms of linear matrix inequalities lmis such conditions are derived by using the leibniz newton formula and free weighting matrix method for fuzzy time delay systems under the assumption that sampling time is not greater than some prescribed number then a design method for a robust h sampled data state feedback controller for uncertain fuzzy systems is proposed numerical examples are given to illustrate our robust h sampled data state feedback control design

robust sampled data stabilization of uncertain fuzzy systems via input delay approach this paper is concerned with robust sampled data stabilization for uncertain fuzzy systems the system is modeled as a continuous time fuzzy system while the control input is a zero order sampled data signal when a zero order control input is considered the closed loop system can be seen as an input delay system hence an input delay system approach is introduced for sampled data control design sufficient stability conditions for the closed loop system are given in terms of linear matrix inequalities lmis under the assumption that sampling interval is not greater than some prescribed number stability conditions for fuzzy time delay systems are given by using jensen s inequality which simplifies conditions with less matrix variables a design method of robust sampled data state feedback controller for uncertain fuzzy systems is then proposed numerical examples are given to illustrate our robust sampled data state feedback control design and to show the effectiveness over other existing results

enriched krylov subspace methods for ill posed problems we describe a modification of the conjugate gradient method for the normal equations cgnr that allows us to enrich the krylov subspaces in which the iterates are determined with vectors containing pertinent information about the desired solution the enriched cgnr method easily can be adapted to the solution of linear systems arising from penalized least squares problems and tikhonov regularization applications to the solution of linear discrete ill posed problems illustrate that enrichment of the krylov subspaces can improve the quality of the computed approximate solutions and reduce the computational effort required for their determination

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

robust mixed h_2 h_infty filtering for time delay fuzzy systems in this paper a robust mixed h2 hinfin filtering problem for continuous time fuzzy systems subject to parameter uncertainties and multiple time varying delays in state variables is addressed the uncertain systems are expressed as takagi sugeno fuzzy models with linear nominal parts and norm bounded uncertainties the main objective is to design stable filters that minimize a guaranteed cost index and achieve a prescribed hinfin performance under worst case disturbance based on lyapunov theory both delay independent and delay dependent sufficient conditions guaranteeing stability and achieving prescribed performances are stated in terms of linear matrix inequalities therefore stable filters can be obtained easily with existing convex algorithms lastly two examples are given to illustrate the proposed design methodology

design of fuzzy controllers for uncertain nonlinear systems using stability and robustness analyses this paper analyzes the stability and robustness of uncertain nonlinear systems and shows that the analysis results provide an efficient technique for the design of fuzzy controllers based on a fuzzy plant model describing an uncertain nonlinear plant this design involves the derivation of a stability criterion and a robust area in the uncertain parameter space in terms of some measures of the closed loop control system matrices an application example on balancing an inverted pendulum is given to illustrate the simple design methodology the stability and the robustness of the feedback system incorporated with the proposed fuzzy controller

h control for sampled data nonlinear systems described by takagi sugeno fuzzy systems in this paper we consider the design problem of output feedback h controllers for sampled data fuzzy systems we first transfer them into equivalent jump fuzzy systems we establish the so called bounded real lemma for jump fuzzy systems and give a design method of suboptimal output feedback h controllers in terms of two riccati inequalities with jumps we then apply the main results to the sampled data fuzzy systems and obtain a design method of suboptimal output feedback h controllers we give a numerical example and construct a suboptimal output feedback h controller

approximation accuracy of the krylov subspaces for linear discrete ill posed problems abstract for the large scale linear discrete ill posed problem min a x b or a x b with b contaminated by gaussian white noise the lanczos bidiagonalization based krylov solver lsqr and its mathematically equivalent cgls the conjugate gradient cg method implicitly applied to a t a x a t b are most commonly used and cgme the cg method applied to min a a t y b or a a t y b with x a t y and lsmr which is equivalent to the minimal residual minres method applied to a t a x a t b have also been choices these methods exhibit typical semi convergence feature and the iteration number k plays the role of the regularization parameter however there has been no definitive answer to the long standing fundamental question can lsqr and cgls find 2 norm filtering best possible regularized solutions the same question is for cgme and lsmr too at iteration k lsqr cgme and lsmr compute different iterates from the same k dimensional krylov subspace a first and fundamental step towards answering the above question is to accurately estimate the accuracy of the underlying k dimensional krylov subspace approximating the k dimensional dominant right singular subspace of a assuming that the singular values of a are simple we present a general sin theorem for the 2 norm distances between these two subspaces and derive accurate estimates on them for severely moderately and mildly ill posed problems we also establish some relationships between the smallest ritz values and these distances numerical experiments justify the sharpness of our results

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

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

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

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

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

robustness design of nonlinear dynamic systems via fuzzy linear control this study introduces a fuzzy linear control design method for nonlinear systems with optimal h sup spl infin robustness performance first the takagi and sugeno fuzzy linear model 1985 is employed to approximate a nonlinear system next based on the fuzzy linear model a fuzzy controller is developed to stabilize the nonlinear system and at the same time the effect of external disturbance on control performance is attenuated to a minimum level thus based on the fuzzy linear model h sup spl infin performance design can be achieved in nonlinear control systems in the proposed fuzzy linear control method the fuzzy linear model provides rough control to approximate the nonlinear control system while the h sup spl infin scheme provides precise control to achieve the optimal robustness performance linear matrix inequality lmi techniques are employed to solve this robust fuzzy control problem in the case that state variables are unavailable a fuzzy observer based h sup spl infin control is also proposed to achieve a robust optimization design for nonlinear systems a simulation example is given to illustrate the performance of the proposed design method

a novel dropout compensation scheme for control of networked t s fuzzy dynamic systems this paper considers the problem of h state feedback control for networked nonlinear systems under unreliable communication links with packet dropouts the nonlinear plant in this paper is described by a takagi sugeno t s fuzzy model the packet dropouts in both sensor to controller s c and controller to actuator c a channels are considered which are modeled by bernoulli processes a new compensation scheme for the estimation of missing packets is proposed and a piecewise state feedback controller is designed so that the resulting closed loop control system is stochastically stable with guaranteed h performance then the results are extended to the case when both network induced delays and packet dropouts exist in communication links finally some numerical examples are given to illustrate the procedure of the proposed approaches and the optimal h performance in comparison to the existing approaches

a fast truncated lagrange method for large scale image restoration problems in this work we present a new method for the restoration of images degraded by noise and spatially invariant blur in the proposed method the original image restoration problem is replaced by an equality constrained minimization problem a quasi newton method is applied to the first order optimality conditions of the constrained problem in each quasi newton iteration the hessian of the lagrangian is approximated by a circulant matrix and the fast fourier transform is used to compute the quasi newton step the quasi newton iteration is terminated according to the discrepancy principle results of numerical experiments are presented to illustrate the effectiveness and usefulness of the proposed method

a novel observer based output feedback controller design for discrete time fuzzy systems this paper addresses the problem of observer based output feedback controller designs for discrete time t s fuzzy systems based on a relaxed approach in which the fuzzy lyapunov functions are used different from the existing two step method a single step linear matrix inequality method is provided for the observer based controller design it is shown that the controller and observer parameters can be obtained by solving a set of strict linear matrix inequalities that are numerically feasible with commercially available software the new design method not only overcomes the drawback induced by the two step approach but also provides less conservative results over some existing results finally the effectiveness of the proposed approach is demonstrated by an example

output stabilization of takagi sugeno fuzzy systems abstract in this paper the output stabilization problem of takagi sugeno fuzzy models is considered first a natural form of observers for such models is given sufficient conditions for their asymptotic convergence are given which are dual to those for the stability of state feedback fuzzy controllers we then show that a state feedback controller and an observer always yield a stabilizing output feedback controller provided that the stabilizing property of the control and the asymptotic convergence of the observer are guaranteed by the lyapunov method using positive definite matrices in this sense it is shown that the separation principle holds for takagi sugeno fuzzy systems two design examples are given to illustrate the theory

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

an approach to h control of fuzzy dynamic systems this paper presents an approach to h control of a class of continuous time nonlinear systems which can be represented by a fuzzy dynamic model a suitable piecewise differentiable quadratic lyapunov function is used to establish asymptotic stability and h performance of the closed loop fuzzy control system a constructive algorithm is developed to obtain the h feedback control law which involves solving a set of suitable algebraic riccati equations an example is given to illustrate the application of the method

arnoldi methods for large sylvester like observer matrix equations and an associated algorithm for partial spectrum assignment abstract we propose an arnoldi based numerical method for solving a sylvester type equation arising in the construction of the luenberger observer given an n n matrix a and an n m matrix g the method simultaneously constructs an m m hessenberg matrix h with a preassigned spectrum and an n m orthonormal matrix x such that ax xh g we consider the case when a is large and sparse so that the standard techniques such as the well known hessenberg schur method for solving a sylvester equation cannot be easily applied as a byproduct we propose an algorithm for the partial pole assignment problem for large matrices

comparing different types of approximators for choosing the parameters in the regularization of ill posed problems regularized approximations to the solutions of ill posed problems typically vary from over smoothed inaccurate reconstructions to under smoothed and unstable solutions as the regularization parameter varies about its optimal value it thus makes sense to compare two or more regularized approximations and seek the parametervalues where the distance between the approximations is a minimum this paper advances the theory and practice of this methodology the method appears to workvery well and be very stable particularly in the presence of extreme error levels

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

robust h sub spl infin disturbance attenuation for a class of uncertain discrete time fuzzy systems the paper is concerned with robust stabilization and h sub spl infin control of a class of uncertain discrete time fuzzy systems the class of uncertain systems is described by state space takagi sugeno ts fuzzy models with linear nominal parts and norm bounded parameter uncertainties in the state and output equations first a sufficient condition on robust stability of the fuzzy models is proposed then h sub spl infin disturbance attenuation performance of the fuzzy models is analyzed some sufficient conditions are derived on robust h sub spl infin disturbance attenuation in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties a numerical example shows the use of the results on the stabilization and h sub spl infin disturbance attenuation of a class of discrete time nonlinear systems via fuzzy switch

galerkin projection methods for solving multiple linear systems in this paper we consider using conjugate gradient cg methods for solving multiple linear systems a i x i b i for 1 le i le s where the coefficient matrices a i and the right hand sides b i are different in general in particular we focus on the seed projection method which generates a krylov subspace from a set of direction vectors obtained by solving one of the systems called the seed system by the cg method and then projects the residuals of other systems onto the generated krylov subspace to get the approximate solutions the whole process is repeated until all the systems are solved most papers in the literature t f chan and w l wan it siam j sci comput 18 1997 pp 1698 1721 b parlett it linear algebra appl 29 1980 pp 323 346 y saad it math comp 48 1987 pp 651 662 v simoncini and e gallopoulos it siam j sci comput 16 1995 pp 917 933 c smith a peterson and r mittra it ieee trans antennas and propagation 37 1989 pp 1490 1493 considered only the case where the coefficient matrices a i are the same but the right hand sides are different we extend and analyze the method to solve multiple linear systems with varying coefficient matrices and right hand sides a theoretical error bound is given for the approximation obtained from a projection process onto a krylov subspace generated from solving a previous linear system finally numerical results for multiple linear systems arising from image restorations and recursive least squares computations are reported to illustrate the effectiveness of the method

nonfragile h_ infty filtering of continuous time fuzzy systems this paper is concerned with the problem of nonfragile h filtering for a class of continuous time fuzzy systems attention is focused on the design of a 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 using the quadratic lyapunov function approach and adding slack matrix variables sufficient conditions for designing the nonfragile h filter are proposed in terms of solutions to a set of linear matrix inequalities lmis finally a simulation example will be given to show the efficiency of the proposed design methods

fuzzy controller design for nonlinear impulsive fuzzy systems with time delay the stabilization problem is investigated for continuous time takagi sugeno t s fuzzy systems with time delay and impulsive effects in this paper some delay independent and delay dependent stabilization approaches are developed for both state feedback and observer based feedback cases which are based on the lyapunov krasovskii functional approach and a parallel distributed compensation scheme the time delay is dealt by lyapunov theory allied with the halanay lemma the restriction on the interval between each impulsive instant and output sampled instant needs not be equal to or less than a constant scalar but it only requires an inequality satisfaction when the impulsive effects vanish the results can be extended to the corresponding sufficient conditions for the cases of a nonlinear continuous time delay system with a state feedback and observer based sampled output feedback finally some examples are given to demonstrate the effectiveness of the proposed method

separation theorems for the zeros of certain hypergeometric polynomials we study interlacing properties of the zeros of two contiguous 2f1 hypergeometric polynomials we use the connection between hypergeometric 2f1 and jacobi polynomials as well as a monotonicity property of zeros of orthogonal polynomials due to markoff to prove that the zeros of contiguous hypergeometric polynomials separate each other we also discuss interlacing results for the zeros of 2f1 and those of the polynomial obtained by shifting one of the parameters of 2f1 by t where 0 t 1

regularization of mellin type inverse problems with an application to oil engineering abstract in this paper we present a novel method for the stable inversion of mellin convolution operators although the inverse operator is explicitly known for this class of operators regularization techniques have to be used due to the ill posedness of the problem considering operators which are continuously invertible between the space l 2 0 and a mellin sobolev space h s 0 we propose a combination of a data smoothing algorithm and an exact inversion for the order optimal regularization of the equation as application we derive the mellin transform of the capillary pressure operator and analyze its mapping properties finally we present some numerical results

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

robust fuzzy controller design for nonlinear multiple time delay systems by dithers this study presents a robustness design of fuzzy control for nonlinear systems with multiple time delays first the neural network nn model is employed to approximate the nonlinear multiple time delay nmtd plant then a linear differential inclusion ldi state space representation is established for the dynamics of the nn model according to the ldi state space representation a robustness design of fuzzy control is proposed to overcome the effect of modeling errors between the nmtd plant and the nn model if the designed fuzzy controller cannot stabilize the nmtd system a dither as an auxiliary of the fuzzy controller is simultaneously introduced to stabilize the nmtd system based on the relaxed method the nmtd system can be stabilized by regulating appropriately the parameters of dither if the frequency of dither is high enough the trajectory of the dithered system and that of its corresponding mathematical model the relaxed system can be made as close as desired this fact enables us to get a rigorous prediction of stability of the dithered system by establishing the stability of the relaxed system

an iterative lagrange method for the regularization of discrete ill posed inverse problems in this paper an iterative method is presented for the computation of regularized solutions of discrete ill posed problems in the proposed method the regularization problem is formulated as an equality constrained minimization problem and an iterative lagrange method is used for its solution the lagrange iteration is terminated according to the discrepancy principle the relationship between the proposed approach and classical tikhonov regularization is discussed results of numerical experiments are presented to illustrate the effectiveness and usefulness of the proposed method

robust stabilization for delayed discrete time fuzzy systems via basis dependent lyapunov krasovskii function abstract this paper deals with the robust control problem for a class of uncertain discrete time fuzzy systems with time delay the uncertainty is assumed to be of structured linear fractional form which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities by using basis dependent lyapunov krasovskii function a robust control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov krasovskii and the system matrices which make the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis the development represents an important step towards reducing the conservatism of previous design methods and the results also generalize earlier works for a more general parametric uncertainty structure numerical examples are also given to demonstrate the applicability of the proposed approach

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

krylov subspace algorithms and circulant embedding method for efficient wideband single carrier equalization wider bandwidth allows higher data rate by transmitting narrower pulses however doing so would also increase the discrete channel memory length for single carrier communication systems this results in higher computational burden at the receiver we are concerned with single carrier nonblock transmission schemes with receiver oversampling as they can provide higher spectral efficiency than block transmission schemes in the presence of large delay spreads we first propose a simple finite impulse response fir equalizer that is based on the circulant embedding ce method and analyze its performance by investigating the relationship between solutions of various finite dimensional models and the original infinite dimensional problem we show that under proper conditions the ce fir equalizer converges exponentially fast to the iir equalizer we then focus on the conjugate gradient cg algorithm as an efficient means for equalization that is specifically well suited for dealing with large delay spread channels we discuss the importance of stopping the iterations for the cg algorithm at the right time in the presence of noise and present several reliable low cost stopping criteria it turns out that the cg algorithm equipped with appropriate stopping criteria can outperform mmse equalizers since both the ce and the cg methods can be efficiently implemented via fast fourier transforms equalization complexity is only in the order of n log n for n data symbols several numerical experiments demonstrate the performance of the proposed methods

h sub spl infin control of discrete time nonlinear systems this paper presents an explicit solution to the problem of disturbance attenuation with internal stability via full information feedback state feedback and dynamic output feedback respectively for discrete time nonlinear systems the h sub spl infin control theory is first developed for affine systems and then extended to general nonlinear systems based on the concepts of dissipation inequality differential game and lasalle s invariance principle in discrete time a substantial difficulty that v a x b x u e x w respectively v f x u w is no longer quadratic in sub w sup u arising in the case of discrete time nonlinear systems has been surmounted in the paper in the case of a linear system we show how the results reduce to the well known ones recently proposed in the literature

h_ infty fuzzy control of nonlinear systems under unreliable communication links this paper investigates the problem of h infin fuzzy control of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s fuzzy model and the control strategy takes the form of parallel distributed compensation the communication links existing between the plant and controller are assumed to be imperfect that is data packet dropouts occur intermittently which appear typically in a network environment and stochastic variables satisfying the bernoulli random binary distribution are utilized to model the unreliable communication links attention is focused on the design of h infin controllers such that the closed loop system is stochastically stable and preserves a guaranteed h infin performance two approaches are developed to solve this problem based on the quadratic lyapunov function and the basis dependent lyapunov function respectively several examples are provided to illustrate the usefulness and applicability of the developed theoretical results

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

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

delay dependent h fuzzy observer based control for discrete time nonlinear systems with state delay this paper studies the h fuzzy observer based control problem for discrete time nonlinear systems with state delay via a fuzzy lyapunov krasovskii functional lkf approach the takagi and sugeno t s fuzzy model is employed to represent a discrete time nonlinear system with state delay based on a non parallel distributed compensation pdc scheme a new fuzzy lkf is first constructed to derive a delay dependent condition such that the closed loop fuzzy system is asymptotically stable and satisfies a prescribed level of h disturbance attenuation in the derivation process two free fuzzy weighting matrices are introduced to express the relationship between the present state and delay state then a novel linear matrix inequality lmi approach is proposed for the design of a delay dependent h fuzzy observer based controller the control and observer matrices can be solved directly by using the existing lmi optimization techniques finally a numerical example is given to illustrate the effectiveness of the proposed design method

piecewise h_ infty controller design of uncertain discrete time fuzzy systems with time delays this paper considers the robust h infin control of uncertain discrete time fuzzy systems with time delays based on piecewise lyapunov krasovskii functionals it is shown that the stability with h infin disturbance attenuation performance can be established for the closed loop fuzzy control systems if there exists a piecewise lyapunov krasovskii functional and moreover the functional and the corresponding controller can be obtained by solving a set of linear matrix inequalities that are numerically feasible a numerical example is given to demonstrate the efficiency and the advantage of the proposed method

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

t s fuzzy model based piecewise h output feedback controller design for networked nonlinear systems with medium access constraint abstract this paper investigates the problem of h output feedback control for a class of networked nonlinear systems subject to medium access constraint where the nonlinear systems are represented by takagi sugeno t s fuzzy models with norm bounded uncertainties the communication constraint concerned is that only one sensor node and one actuator node can access the shared network which is the case in network environment the accessibility of sensor nodes and or actuator nodes is determined by medium access control with a prescribed probability the attention is focused on the design of a piecewise static output feedback controller such that the closed loop control system is stochastically stable with a guaranteed h performance based on piecewise quadratic lyapunov functions together with some matrix inequality convexifying techniques an approach to the design of h output feedback controller is proposed in terms of linear matrix inequalities finally two simulation examples are provided to illustrate the effectiveness of the proposed methods

h sub infinity analysis and synthesis of discrete time systems with time varying uncertainty the problems of h sub infinity analysis and synthesis of discrete time systems with block diagonal real time varying uncertainty are considered it is shown that these problems can be converted into scaled h sub infinity analysis and synthesis problems the problems of quadratic stability analysis and quadratic stabilization of these types of systems are dealt with as a special case the results on synthesis are established for general linear dynamic output feedback control

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

reduced sqp methods for parameter identification problems parameter estimation problems are formulated as constrained regularized optimization problems reduced sqp methods with bfgs update are analyzed to solve these infinite dimensional optimization problems rate of convergence results are given and numerical feasibility of the resulting algorithms is demonstrated

guaranteed cost control of affine nonlinear systems via partition of unity method we consider the problem of guaranteed cost control gcc of affine nonlinear systems in this paper firstly the general affine nonlinear system with the origin being its equilibrium point is represented as a linear like structure with state dependent coefficient matrices secondly partition of unity method is used to approximate the coefficient matrices as a result of which the original affine nonlinear system is equivalently converted into a linear like system with modeling error a gcc law is then synthesized based on the equivalent model in the presence of modeling error under certain error condition the control law ensures that the system under control is asymptotically stable as well as that a given cost function is upper bounded a suboptimal gcc law can be obtained via solving an optimization problem in terms of linear matrix inequality lmi in stead of state dependent riccati equation sdre or hamilton jacobi equations that are usually required in solving nonlinear optimal control problems finally a numerical example is provided to illustrate the validity of the proposed method

zeros of 3 f 2 hypergeometric polynomials abstract we investigate the behaviour of the zeros of three distinct types of 3 f 2 hypergeometric polynomials each type of polynomial considered has degree 2 n and contains a free parameter b we describe the location of the zeros as b varies continuously through real values numerical tables of the zeros generated by mathematica are presented in confirmation of our stated results

spl hscr sub spl infin control of nonlinear systems a convex characterization the nonlinear spl hscr sub spl infin control problem is considered with an emphasis on developing machinery with promising computational properties the solutions to spl hscr sub spl infin control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems the computational implications for the characterization are discussed

cal h _ infty state feedback control design for fuzzy systems using lyapunov functions with quadratic dependence on fuzzy weighting functions this paper proposes a method for designing an hinfin state feedback fuzzy controller for discrete time takagi sugeno t s fuzzy systems to derive less conservative hinfin stabilization conditions this paper enhances the interactions among the fuzzy subsystems using a multiple lyapunov function with quadratic dependence on fuzzy weighting functions besides for more allocation of the nonlinearity to the fuzzy control system this paper introduces a slack variable that is quadratically dependent on the one step past fuzzy weighting functions as well as the current ones in the derivation the hinfin stabilization conditions are formulated in terms of parameterized linear matrix inequalities plmis which are reconverted into lmi conditions with the help of an efficient relaxation technique

robust stability analysis and fuzzy scheduling control for nonlinear systems subject to actuator saturation takagi sugeno ts fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output submodels in this paper the ts fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation the ts fuzzy representation of a nonlinear system subject to actuator saturation is presented in our ts fuzzy representation the modeling error is also captured by norm bounded uncertainties a set invariance condition for the system in the ts fuzzy representation is first established based on this set invariance condition the problem of estimating the domain of attraction of a ts fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality lmi optimization problem by viewing the state feedback gain as an extra free parameter in the lmi optimization problem we arrive at a method for designing state feedback gain that maximizes the domain of attraction a fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction an inverted pendulum is used to show the effectiveness of the proposed fuzzy controller

robust stabilization of uncertain systems with time varying multistate delay the authors deal with the problem of stabilizing a class of uncertain linear systems with time varying multi state delay and subject to norm bounded parameter uncertainty via memoryless linear state feedback some sufficient conditions for the robust stabilizability are derived fur this class of uncertain systems if there exists a positive definite symmetric solution satisfying the algebraic riccati equation or inequality a suitable memoryless state feedback law can be derived also moreover all such parametric algebraic riccati inequalities have been transformed into some linear matrix inequality problems so there is no tuning of the parameters to gain a stabilizing solution

robust fuzzy control for uncertain discrete time nonlinear markovian jump systems without mode observations this paper studies the robust fuzzy control problem of uncertain discrete time nonlinear markovian jump systems without mode observations the takagi and sugeno t s fuzzy model is employed to represent a discrete time nonlinear system with norm bounded parameter uncertainties and markovian jump parameters as a result an uncertain markovian jump fuzzy system mjfs is obtained a stochastic fuzzy lyapunov function flf is employed to analyze the robust stability of the uncertain mjfs which not only is dependent on the operation modes of the system but also directly includes the membership functions then based on this stochastic flf and a non parallel distributed compensation non pdc scheme a mode independent state feedback control design is developed to guarantee that the closed loop mjfs is stochastically stable for all admissible parameter uncertainties the proposed sufficient conditions for the robust stability and mode independent robust stabilization are formulated as a set of coupled linear matrix inequalities lmis which can be solved efficiently by using existing lmi optimization techniques finally it is also demonstrated via a simulation example that the proposed design method is effective

robust h control for discrete time fuzzy systems via basis dependent lyapunov functions this paper deals with the robust h control problem for a class of discrete time fuzzy systems with uncertainty the uncertainty is assumed to be of structured linear fractional form by using basis dependent lyapunov function an h control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov and the system matrices which makes the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis it is expected that the basis dependent results are less conservative than the basis independent ones due to the introduction of basis dependent lyapunov function finally numerical examples including the discrete chaotic lorenz system are also given to demonstrate the applicability of the proposed approach

fast cg based methods for tikhonov phillips regularization tikhonov phillips regularization is one of the best known regularization methods for inverse problems a posteriori criteria for determining the regularization parameter alpha require solving a a alpha i x a y delta for different values of alpha we investigate two methods for accelerating the standard cg algorithm for solving the family of systems the first one utilizes a stopping criterion for the cg iterations which depends on alpha and delta the second method exploits the shifted structure of the linear systems which allows us to solve simultaneously for different values of alpha we present numerical experiments for three test problems which illustrate the practical efficiency of the new methods the experiments as well as theoretical considerations show that run times are accelerated by a factor of at least 3

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

asymptotic distributions of the zeros of certain classes of gauss hypergeometric polynomials abstract we study the asymptotic distribution of the zeros of certain classes of gauss hypergeometric polynomials classical analytic methods such as watson s lemma and the method of steepest descents are used to analyze the large n behavior of the zeros of the gauss hypergeometric polynomials 2 f 1 n a kn b z 2 f 1 n kn c kn c z and 2 f 1 n pn z where n is a nonnegative integer the constants k a 0 p 1 and b c r owing to the connection between jacobi polynomials and gauss hypergeometric polynomials we prove a special case of a conjecture made by martinez finkelshtein martinez gonzalez and orive numerical evidence and graphical illustrations of the clustering of zeros on certain curves are generated by mathematica version 4 0

recycling subspace information for diffuse optical tomography we discuss the efficient solution of a long sequence of slowly varying linear systems arising in computations for diffuse optical tomographic imaging the reconstruction of three dimensional absorption and scattering information by matching computed solutions from a parameterized model to measured data leads to a nonlinear least squares problem that we solve using the gauss newton method with a line search this algorithm requires the solution of a long sequence of linear systems each choice of parameters in the nonlinear least squares algorithm results in a different matrix describing the optical properties of the medium these matrices change slowly from one step to the next but may change significantly over many steps for each matrix we must solve a set of linear systems with multiple shifts and multiple right hand sides for this problem we derive strategies for recycling krylov subspace information that exploit properties of the application and the nonlinear optimization algorithm to significantly reduce the total number of iterations over all linear systems furthermore we introduce variants of gcro that exploit symmetry and that allow simultaneous solution of multiple shifted systems using a single krylov subspace in combination with recycling although we focus on a particular application and optimization algorithm our approach is applicable generally to problems where sequences of linear systems must be solved this may guide other researchers to exploit the opportunities of tunable solvers we provide results for two sets of numerical experiments to demonstrate the effectiveness of the resulting method

flexible and deflated variants of the block shifted gmres method abstract the solution of linear systems with multiple shifts and multiple right hand sides given simultaneously is required in many large scale scientific and engineering applications in this paper we introduce new flexible and deflated variants of the shifted block gmres method for this problem class the proposed methods solve the whole sequence of linear systems simultaneously detecting effectively the linear systems convergence and allowing the use of variable preconditioning which may be particularly useful in some applications numerical experiments are illustrated to show the overall significant robustness of the iterative method for solving general sparse multi shifted and multiple right hand side systems and in realistic pagerank calculations to the best of our knowledge this is the first krylov subspace method that combines deflation techniques and variable preconditioning for solving sequences of multi shifted linear systems with multiple right hand sides simultaneously

the fuzzy discrete time robust regulation problem an lmi approach this paper is concerned with the design of a robust regulator capable of achieving trajectory tracking for discrete time nonlinear systems under parameter uncertainty by assuming that the behavior of the nonlinear system is described at least locally by a takagi sugeno dynamic fuzzy model an approach based in the combination of this fuzzy modeling and the regulator theory is presented conditions for the existence of a robust regulator under this approach are then derived and extended to include the use of the linear matrix inequality lmi technique

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

robust passivity and passification of stochastic fuzzy time delay systems in this paper the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time varying delays the fuzzy system is based on the takagi sugeno t s model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning to reflect more realistic dynamical behaviors of the system both the parameter uncertainties and the stochastic disturbances are considered where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a brownian motion we first propose the definition of robust passivity in the sense of expectation then by utilizing the lyapunov functional method the ito differential rule and the matrix analysis techniques we establish several sufficient criteria such that for all admissible parameter uncertainties and stochastic disturbances the closed loop stochastic fuzzy time delay system is robustly passive in the sense of expectation the derived criteria which are either delay independent or delay dependent are expressed in terms of linear matrix inequalities lmis that can be easily checked by using the standard numerical software illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results

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

h filtering of discrete time fuzzy systems via basis dependent lyapunov function approach this paper is concerned with the h filtering problem for a class of discrete time fuzzy systems attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the h sense by using basis dependent lyapunov functions sufficient conditions for the solvability of this problem are obtained it has been shown that the h filtering problem can be solved as a linear matrix inequality lmi optimization problem two examples are provided to demonstrate the applicability of the proposed approach

restarted gmres for shifted linear systems shifted matrices which differ by a multiple of the identity only generate the same krylov subspaces with respect to any fixed vector this fact has been exploited in lanczos based methods like cg qmr and bicg to simultaneously solve several shifted linear systems at the expense of only one matrix vector multiplication per iteration here we develop a variant of the restarted gmres method exhibiting the same advantage and we investigate its convergence for positive real matrices in some detail we apply our method to speed up multiple masses calculations arising in lattice gauge computations in quantum chromodynamics one of the most time consuming supercomputer applications

robust disturbance attenuation with stability for linear systems with norm bounded nonlinear uncertainties in this paper the problem of robust stabilization and robust disturbance attenuation is investigated for systems with linear nominal parts and norm bounded nonlinear uncertainties on both states and control inputs it is shown that the type of nonlinear uncertainty sets considered in this paper has an equivalent representation by linear uncertainty sets based on this key result and some standard riccati inequality approaches for robust control of linear uncertain systems a constructive design procedure is developed

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

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

fuzzy model based control of complex plants in the field of fuzzy modeling the takagi sugeno fuzzy model has been used to approximate accurately the dynamics of complex plants the paper addresses two control design problems associated with state space realizations of such fuzzy models first we treat the stability robustness of fuzzy model based controllers against modeling uncertainty second we develop observer based control schemes and further investigate the behavior of estimated state feedback in both cases we provide sufficient conditions that guarantee stability of the closed loop the results are demonstrated on the fuzzy model of a gas furnace process

analysis and design of fuzzy control systems using dynamic fuzzy state space models a discrete time fuzzy control system which is composed of a dynamic fuzzy model and a fuzzy state feedback controller is proposed stability of the fuzzy control system is discussed and two sufficient conditions to guarantee the stability of the system are given in terms of uncertain linear system theory an algorithm is developed to check the stability condition the controller design method is divided into two procedures one is to get the state feedback matrix by linear system theory in every local rule map the other is to determine conditions of global stability by using a nonlinear analysis method two examples are used to show the design method

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

stability analysis of discrete time fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a stability analysis method for discrete time takagi sugeno fuzzy dynamic systems based on a piecewise smooth lyapunov function it is shown that the stability of the fuzzy dynamic system can be established if a piecewise lyapunov function can be constructed and moreover the function can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software it is also demonstrated via numerical examples that the stability result based on the piecewise quadratic lyapunov functions is less conservative than that based on the common quadratic lyapunov functions

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

delay dependent stability and h control for a class of fuzzy descriptor systems with time delay this paper addresses issues of stability analysis and h control for a class of fuzzy time delay descriptor systems described by an extended takagi sugeno t s fuzzy model a delay dependent stability criterion is first presented and a h control synthesis approach is then developed both the stability criterion and the h controller synthesis are based on the solutions of linear matrix inequalities lmis finally two examples are given to illustrate the effectiveness of the approaches proposed in this paper

interlacing of zeros of shifted sequences of one parameter orthogonal polynomials we study the interlacing property of zeros of laguerre polynomials of adjacent degree where the free parameters differ by an integer and of the same degree where the free parameter is shifted continuously similar interlacing results are proven for the positive zeros of gegenbauer polynomials

decentralized h_ infty filter design for discrete time interconnected fuzzy systems this paper describes a decentralized h infin filter design for discrete time interconnected fuzzy systems based on piecewise quadratic lyapunov functions the systems consist of j discrete time interconnected takagi sugeno t s fuzzy subsystems and a decentralized h infin filter is designed for each subsystem it is shown that the stability of the overall filtering error system with h infin performance can be established if a piecewise quadratic lyapunov function can be constructed moreover the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible two simulation examples are given to show the effectiveness of the proposed approach