on stabilization for discrete linear time varying systems abstract in this paper we consider the stabilization problem for discrete linear time varying systems in an operator theoretic framework by using the complete finiteness of a certain discrete nest algebra we show that a system is stabilizable if and only if it has one kind of strong representation and we also give a parametrization for all the stabilizing controllers in terms of this strong representation this result extends the youla parametrization theorem by only requiring a strong left or a strong right representation but not both the strong stabilization problem is also discussed

the largest singular value of e sup x a sub 0 e sup x is convex on convex sets of commuting matrices a short and direct proof of the convexity property is given it is shown that the theorem applies to any convex commuting set of matrices in r sup nxn where a sub 0 in r sup nxn is fixed it is also shown that the result does not hold if x is permitted to be a general square matrix a counterexample is supplied for noncommuting matrices

time varying versus time invariant compensation for rejection of persistent bounded disturbances and robust stabilization it is shown that time varying compensation does not improve the optimal rejection of persistent bounded disturbances this result is obtained by exploiting a key observation that any time varying compensator which yields a given degree of disturbance rejection must do so uniformly over time thereby removing any advantage of time variation this key observation is exploited to show that time varying compensation does not improve the optimal rejection of disturbances regardless of the norm used to measure the disturbances thus absolutely summable finite energy or persistent bounded disturbances may be treated in the same manner it is shown that time varying compensation does not help in the bounded input bounded output robust stabilization of time invariant plants with unstructured uncertainty in doing so it is also shown that the small gain theorem is both necessary and sufficient for the bounded input bounded output stability of certain linear time varying plants subject to unstructured linear time varying perturbations

robust h disturbance minimization by duality abstract the nonstandard optimization problem inf sup w i pq e i vpq e i 0 2 q h n n plays a basic role in robust feedback analysis here its solutions are characterized using banach space duality theory and shown to satisfy a flatness or allpass condition

optimal h robustness and the relationship to lqg design problems a solution to the hx optimal control problem is obtained by employing a standard lqg polynomial based solution procedure the derivation is straightforward and avoids many of the more abstract mathematical results usually employed the relationship between the lqg and hm design methods becomes transparent and the similarities and differences can be identified

on the resonance structure in a forced excitable system the dynamics of forced excitable systems are studied analytically and numerically with a view toward understanding the resonance or phase locking structure in a singular limit the system studied reduces to a discontinuous flow on a two torus which in turn gives rise to a set valued circle map it is shown how to define rotation numbers for such systems and derive properties analogous to those known for smooth flows the structure of the phase locking regions for a fitzhugh nagumo system in the singular limit is also analyzed a singular perturbation argument shows that some of the general results persist for the nonsingularly perturbed system and some numerical results on phase locking in the forced fitzhugh nagumo equations illustrate this fact the results explain much of the phase locking behavior seen experimentally and numerically in forced excitable systems including the existence of threshold stimuli for phase locking the results are compared with known results for forced oscillatory systems

non uniform elliptic equations in convex lipschitz domains abstract non uniform elliptic equations in convex lipschitz domains are concerned the non smooth domains consist of a periodic connected high permeability sub region and a periodic disconnected matrix block subset with low permeability let 0 1 denote the size ratio of the matrix blocks to the whole domain and let 2 0 1 denote the permeability ratio of the disconnected matrix block subset to the connected sub region the w 1 p norm for p 1 of the elliptic solutions in the high permeability sub region is shown to be bounded uniformly in however the w 1 p norm of the solutions in the low permeability subset may not be bounded uniformly in roughly speaking if the sources in the low permeability subset are small enough the solutions in that subset are bounded uniformly in otherwise the solutions cannot be bounded uniformly in relations between the sources and the variation of the solutions in the low permeability subset are also presented in this work

factorization in analytic operator algebras abstract a constructive and unified approach is used to obtain the upper lower factorization of positive operators and the outer function factorization of positive operator valued functions on the circle for a projection nest e it is shown that every positive operator admits a canonical factorization c a a with a an outer operator if and only if e is well ordered with new methods we generalize the inner outer factorizations obtained by arveson for nests of order type z and the riesz factorization due to shields for trace class triangular operators weak factorization is obtained in noncommutative h1 spaces associated with general nest subalgebras of a semifinite factor characterizations of a nehari type are given for the associated hankel forms and hankel operators

interior regularity estimates in high conductivity homogenization and application in this paper uniform pointwise regularity estimates for the solutions of conductivity equations are obtained in a unit conductivity medium reinforced by an e periodic lattice of highly conducting thin rods the estimates are derived only at a distance e1 for some 0 away from the fibres this distance constraint is rather sharp since the gradients of the solutions are shown to be unbounded locally in lp as soon as p 2 one key ingredient is the derivation in dimension two of regularity estimates to the solutions of the equations deduced from a fourier series expansion with respect to the fibres direction and weighted by the high contrast conductivity the dependence on powers of e of these two dimensional estimates is shown to be sharp the initial motivation for this work comes from imaging and enhanced resolution phenomena observed experimentally in the presence of micro structures lerosey et al science 315 1120 1124 2007 we use these regularity estimates to characterize the signature of low volume fraction heterogeneities in the fibred reinforced medium assuming that the heterogeneities stay at a distance e1 away from the fibres

entropy minimizing and risk sensitive control rules abstract glover and doyle 4 have shown that the entropy minimising criterion is identical with the infinite horizon form of the leqg optimality criterion leqg linear exponential of quadratic gaussian whittle and kuhn 11 have given a hamiltonian formulation which provides a natural treatment of leqg optimisation this paper contains a direct proof that the control yielded by these hamiltonian methods is entropy minimising the conclusion would follow from the two assertions above but a simple adjoining of the proofs of these two assertions yields an argument so circuitous that a direct proof is of interest

analysis of time varying control strategies for optimal disturbance rejection and robustness analysis of linear time invariant systems that are controlled by time varying controllers is given the problems of disturbance rejection and robustness are formulated and analyzed using functional analytic methods which reveal the properties that are common to these problems the theoretical development presented uses the theory and techniques of nuclear operators and their relation with the duality theory of tensor products of banach spaces the authors show how time varying compensation offers no advantage over time invariant compensation for the problem of disturbance rejection over general signal spaces in both continuous and discrete time and for the problem of l sub infinity robust stabilization of time invariant plants in addition another application of the theory for the problem of norm minimization subject to a norm constraint is presented

optimal model matching control for time delay systems model matching control for time delay systems is formulated as an optimization problem in h2 norm space as well as h norm space wiener hopf techniques and the theory of optimal interpolation are successfully employed to treat this model matching problem including perfect and imperfect model matching cases prior to this work for time delay systems only the problem of perfect model matching control had been considered and no attempt had been made to examine that of imperfect model matching control with the optimization approach presented here an optimal model matching control scheme is constructed for the imperfect model matching case to produce perfect model matching results whenever possible

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

non local homogenized limits for composite media with highly anisotropic periodic fibres we consider a homogenization problem for highly anisotropic conducting fibres embedded into an isotropic matrix for a double porosity type scaling in the expression of high contrast between the conductivity along the fibres and the conductivities in the transverse directions we prove the homogenization theorem and derive two scale homogenized equations using a version of the method of two scale convergence supplemented in the case when the spectral parameter 0 by a newly derived variant of high contrast poincare type inequality further elimination of the rapid component from the two scale limit equations results in a non local convolution type integro differential equation for the slowly varying part in the matrix with the non local kernel explicitly related to the green function on the fibre the regularity of the solution to the non local homogenized equation is proved

sampled data control of continuous time systems with an h optimality criterion abstract the synthesis of sampled data controllers for continuous time systems is studied in the context of h control theory the sampled data h optimal control problem consists of finding a sampled data controller which minimizes the l2 induced norm from the continuous time disturbance to the continuous time output the problem is here solved via a discrete system representation this is achieved by describing the closed loop system as a discrete system with finite state dimension and with a representation of the disturbance and the output signals of the discrete system as sequences of elements of certain infinite dimensional spaces via finite rank approximations of a compact integral operator associated with the system the sampled data h control problem can be solved to any degree of accuracy from the structure of the problem it follows that irrespective of the order of the approximation a feasible sampled data controller can be found which has the same order as the system

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

performance robustness of discrete time systems with structured uncertainty given an interconnection of a nominal discrete time plant and a stabilizing controller together with structured norm bounded nonlinear time varying perturbations necessary and sufficient conditions for robust stability and performance of the system are provided it is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem the resulting stability robustness problem is shown to be equivalent to a simple algebraic one the solution of which provides the desired necessary and sufficient conditions for performance stability robustness these conditions provide an effective tool for robustness analysis and can be applied to a large class of problems in particular it is shown that some known results can be obtained immediately as special cases of these conditions

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

duality theory for mimo robust disturbance rejection banach space duality theory is used to characterize the solutions of a nonstandard h sup infinity optimization problem which is shown to be allpass in general and unique in the single input single output siso ease the theory leads to a numerical solution of duality and convex optimization which is applied to an example for a limiting case of sharp cutoff filters an explicit solution of the optimal robust disturbance attenuation problem ordap resembling the two arc theorem of complex analysis is derived

weight selection in feedback design with degree constraints we present an approach for feedback design which is based on recent developments in analytic interpolation with a degree constraint performance is cast as an interpolation problem with bounded analytic functions minimizers of a certain weighted entropy functional provide interpolants having degree less than the number of constraints the choice of weight parameterizes all such bounded degree solutions however the relationship between the weights and the shape of corresponding transfer functions is not direct thus in this paper we develop a formalism that guides weight selection

output feedback decentralized control of large scale systems using weighted sensitivity functions minimization this paper considers the problem of achieving stability and desired dynamical transient behavior for linear large scale systems by decentralized control it can be done by making the effects of the interconnections between the subsystems arbitrarily small sufficient conditions for stability and diagonal dominance of the closed loop system are introduced these conditions are in terms of decentralized subsystems and directly make a constructive h control design possible a mixed h pole region placement is suggested such that by assigning the closed loop eigenvalues of the isolated subsystems appropriately the eigenvalues of the overall closed loop system are assigned in desirable range the designs are illustrated by an example

h control with transients in h infty or uniformly optimal control problems it is usually assumed that the system initial conditions are zero in this paper an h infty like control problem that incorporates uncertainty in initial conditions is formulated this is done by defining a worst case performance measure both finite and infinite horizon problems are considered necessary and sufficient conditions are derived for the existence of controllers that yield a closed loop system for which the above mentioned performance measure is less than a prespecified value state space formulae for the controllers are also presented

robust stability with time varying structured uncertainty considers the problem of assessing robust stability in the presence of block diagonally structured time varying dynamic uncertainty it is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition the notion of stability here is finite gain stability over finite energy signals in sharp contrast to the case of time invariant dynamic uncertainty this result is not limited by the number uncertainty blocks these results parallel previous results regarding finite gain stability over persistent bounded signals

resonance in excitable systems under step function forcing ii subharmonic solutions and persistence abstract in an earlier paper othmer and watanabe 1994 we studied the existence and stability of harmonic solutions in a fitzhugh nagumo type model under step function forcing in this paper we study subharmonic solutions and show that a number of phenomena arise which do not occur in invertible circle maps in particular we show that the rotation number may be non monotonic or discontinuous in one parameter families and that stable periodic solutions with different rotation numbers coexist on open sets in parameter space the latter result shows how an experimental observation first due to mines 1913 can be understood in the context of a flow we also show that the table results for the singular system persist in the non singular system in a sense made precise later

bifurcation analysis of a periodically forced relaxation oscillator differential model versus phase resetting map we compare the dynamics of the periodically forced fitzhugh nagumo oscillator in its relaxation regime to that of a one dimensional discrete map of the circle derived from the phase resetting response of this oscillator the phase resetting map the forcing is a periodic train of gaussian shaped pulses with the width of the pulses much shorter than the intrinsic period of the oscillator using numerical continuation techniques we compute bifurcation diagrams for the periodic solutions of the full differential equations with the stimulation period being the bifurcation parameter the period 1 solutions which belong either to isolated loops or to an everywhere unstable branch in the bifurcation diagram at sufficiently small stimulation amplitudes merge together to form a single branch at larger stimulation amplitudes as a consequence of the fast slow nature of the oscillator this merging occurs at virtually the same stimulation amplitude for all the period 1 loops again using continuation we show that this stimulation amplitude corresponds in the circle map to a change of topological degree from one to zero we explain the origin of this coincidence and also discuss the translational symmetry properties of the bifurcation diagram

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

transitivity in simultaneous stabilization for a family of time varying systems abstract this paper develops necessary and sufficient conditions for the so called transitivity and strong transitivity precise definitions later for a family of discrete time varying linear systems which when satisfied lead to characterizations for simultaneous stabilizability and simultaneously stabilizing feedback controllers some criteria for the strong transitivity are established in terms of single coprime factorizations of only one plant and one controller the resulting characterization involves coprime factorizations of fewer systems compared to previous work

linear elliptic equations in composite media with anisotropic fibres abstract linear elliptic equations in composite media with anisotropic fibres are concerned the media consist of a periodic set of anisotropic fibres with low conductivity included in a connected matrix with high conductivity inside the anisotropic fibres the conductivity in the longitudinal direction is relatively high compared with that in the transverse directions the coefficients of the elliptic equations depend on the conductivity this work is to derive the holder and the gradient l p estimates uniformly in the period size of the set of anisotropic fibres as well as in the conductivity ratio of the fibres in the transverse directions to the connected matrix for the solutions of the elliptic equations furthermore it is shown that inside the fibres the solutions have higher regularity along the fibres than in the transverse directions

two properties of l sub 1 optimal controllers the solution of the l sub 1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better known h infinity sensitivity minimization problem or the lqg linear quadratic gaussian problem is given of a one parameter family of first order plants where the order of the l sub 1 optimal compensator can be arbitrarily large and thus it is impossible to bound the order of an l sub 1 optimal compensator in terms of the order of the plant a plant is considered which has a continuous one parameter family of l sub 1 optimal compensators and thus l sub 1 optimal compensators need not be unique the author s two examples are considered to answer two questions left open by m a daleh and j b pearson ibid vol 32 p 314 23 1987

h2 optimal control of linear systems with tracking disturbance rejection constraints this paper considers the design of two degree of freedom linear multivariable controllers for four block matrix transfer functions with objectives pertaining to both random and deterministic signals the former are taken into account in the cost functional whereas the latter entail that the controller is constrained to solve a servomechanism problem involving a class of reference signals and two classes of disturbances the cost functional is set up by adding quadratic terms to the usual lqg wiener hopf cost in such a way as to ensure the existence of unique solutions even when the signals to be tracked rejected as well as models have poles on the imaginary axis the solutions of the servomechanism problem are explicitly parametrized by free stable rational and proper parameters under two sets of assumptions one which is necessary and sufficient for the existence of solutions and another stronger set which avoids kronecker products and the associated higher dimensional factorizations involved in

mimo disturbance and plant uncertainty attenuation by feedback this paper investigates the ability of feedback to reduce plant and disturbance uncertainties in the multiple input multiple output mimo case by solving two fundamental problems posed by zames in the late seventies the first problem is termed the mimo extension of the optimal robust disturbance attenuation problem the second is a filtering of plant uncertainty two degree of freedom feedback problem the optimal solutions of these problems are characterized using banach space duality theory and shown to satisfy an allpass condition and an extremal identity moreover the duality description leads to a dual pair of optimizations and the introduction of two nonstandard matrix norms in particular the primal dual optimization reduces naturally to approximate finite dimensional convex optimizations within desired tolerance whereas the computation of the nonstandard matrix norms are shown to be equivalent to specific semi definite programming problems and a numerical solution based on convex programming is provided it is also shown using douglas range inclusion theorem that performance is a monotonic function of uncertainty and some qualitative implications for feedback are derived

on the minimization of sensitivity to additive disturbances for linear distributed parameter mimo feedback systems the problem of minimizing the sensitivity of the output or input of a plant under a feedback control with respect to external additive disturbances is considered the mathematical model assumed for the plant is a rectangular matrix of transfer functions which can arise from both lumped parameter and distributed parameter systems including time delays the feedback controller is assumed to guarantee the closed loop stability it is shown that an arbitrarily small sensitivity function on a compact set of complex frequencies can be obtained by a suitable choice of feedback transfer function provided no zero of the plant transfer function is in this set additionally the sensitivity function can be designed to be bounded on an unbounded region containing the imaginary axis if there are no zeros of the plant in the right half plane and a certain hypothesis holds multiplicative delays are not excluded if there are zeros in the right half plane the latter design is not realizable since minimizing the sen

operator theoretic approach to the optimal two disk problem the nonstandard two disk problem plays a fundamental role in robust feedback optimization here it is shown via banach space duality theory that its solutions satisfy an extremal identity and may be viewed as a dual extremal kernel of a particular l sup 1 optimization problem a novel operator theoretic framework to characterize explicitly its solutions is developed in particular the two disk optimization is shown to be equal to the induced norm of a specific operator defined on a projective tensor product space involving a non hilbert version of a vector valued h sup 2 space moreover this operator is shown to be a combination of multiplication and toeplitz operators under certain conditions existence of maximal vectors is established leading to an explicit formula for the optimal controller an infinite matrix representation with respect to a canonical basis is derived together with an algorithm to compute it the norm of the relevant operator is approximated by special finite dimensional optimizations whose solutions lead to solving semi definite programming problems involving the computation of a matrix projective tensor norm

linear feedback systems and the graph topology it is established for general linear systems that the gap metric induces the coarsest topology with respect to which both closed loop stability and closed loop performance are robust properties in earlier works similar topological results were obtained by exploiting the existence of particular coprime factor system representations not known to exist in general by contrast the development here does not rely on any specific system representations systems are simply characterized as subspaces of norm bounded input output pairs and the analysis hinges on the underlying geometric structure of the feedback stabilization problem unlike other work developed within such a framework fundamental issues concerning the causality of feedback interconnections are discussed explicitly the key result of this paper concerns the difference between linear feedback interconnections with identical controllers in terms of a performance robustness related closed loop mapping upper and lower bounds on the induced norm of this difference are derived allowing for possibly infinite dimensional input output spaces and time varying behavior the bounds are both proportional to the gap metric distance between the plants which clearly demonstrates the gap to be an appropriate measure of the difference between open loop systems from the perspective of closed loop behavior to conclude an example is presented to show that bounds of the form derived here for linear systems do not hold in a general nonlinear setting

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

further results on limitations to the capability of feedback in this paper we study the limitations of the capability of the feedback mechanism in dealing with structural uncertainty for a class of pth order non linear autoregressive control systems the size of the structural uncertainty is characterized by multiple lipschitz constants say l 1 l 2 lp of the uncertain non linear function it is shown that if l 1 l 2 lp satisfy certain algebraic conditions then there exists no globally stabilizing feedback control law for the corresponding uncertain systems the result here is an extension of the previous result obtained by zhang and guo 2002

optimal sensitivity theory for multivariate distributed plants in this note we generalized the results of foias and tannenbaum 1986 a and foias et al 1987 on optimal sensitivity minimization to a much broader class of distributed plants we relate our results to certain kinds of hankel norm approximation problems that frequently appear in control engineering applications

time varying optimal disturbance minimization in presence of plant uncertainty the optimal robust disturbance rejection problem plays an important role in feedback control theory here its time varying version is solved explicitly in terms of duality and operator theory in particular the optimum is shown to satisfy a time varying allpass property moreover optimal performance is given in terms of the norm of a bilinear form the latter depends on a lower triangular projection and a multiplication operator defined on special versions of spaces of compact operators

an approach to h control of a class of nonlinear systems this paper considers robust h control of a class of nonlinear systems that can be represented by a heterogeneous model a new controller design method using both state feedback is proposed based on quadratic stability theory a number of necessary and sufficient conditions are derived for quadratic stabilizability with disturbance attenuation of the control system concerned an example is also given to demonstrate the performance of the proposed controller design methods

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

infinite horizon h control for nonlinear stochastic markov jump systems with x u v dependent noise via fuzzy approach in this paper the h control problem is studied for nonlinear stochastic markov jump systems with state control and external disturbance dependent noise x u v dependent noise for short a sufficient condition is derived for the infinite horizon h control of such systems in terms of a set of coupled second order hamilton jacobi inequalities hjis in general it is difficult to solve these coupled hjis by using fuzzy approach the infinite horizon h control design for nonlinear stochastic markov jump systems is developed via solving a set of linear matrix inequalities lmis instead of hjis two numerical examples are presented to illustrate the effectiveness of the proposed design methods