stochastic differential inclusions and diffusion processes connections between weak solutions of stochastic differential inclusions and solutions of partial differential inclusions generated by given set valued mappings are considered the main results are based on some continuous approximation selection theorem and weak compactness of the set of all weak solutions to a given stochastic differential inclusion

quadratic stability and stabilization of uncertain linear discrete time systems with state delay abstract this paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete time systems with state delay the system under consideration involves state time delay and time varying norm bounded parameter uncertainties appearing in all the matrices of the state space model necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities respectively a robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities two examples are presented to demonstrate the effectiveness of the proposed approach

on set valued stochastic integrals and fuzzy stochastic equations in this paper we extend the notion of set valued and fuzzy stochastic integrals to semimartingale integrators we present their main properties and finally we establish the existence of solutions of a fuzzy integral stochastic equation driven by a brownian motion the approach is based on the existence of solutions of an appropriately formulated martingale problem for a system of stochastic inclusions and the theorem of negoita and ralescu

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

robust observer design for ito stochastic time delay systems via sliding mode control this paper deals with the output feedback sliding mode control for ito stochastic time delay systems the system states are unmeasured and the uncertainties are unmatched a sliding mode control scheme is proposed based on the state estimates by utilizing a novel switching function the derivative of the switching function is ensured to be finite variation it is shown that the sliding mode in the estimation space can be attained in finite time the sufficient condition for the asymptotic stability in probability of the overall closed loop stochastic system is derived finally a simulation example is shown to illustrate the proposed method

non fragile asynchronous h control for uncertain stochastic memory systems with bernoulli distribution abstract this study constructs and investigates the non fragile asynchronous h control for uncertain stochastic memory systems with bernoulli distribution the system not only contains the randomly occurring uncertainties of all parameters rouaps and stochastic disturbances in the system model but also includes randomly gain perturbations in the controller by introducing the stochastic variables a new model structure is built obeying bernoulli distribution to describe the system and the controller moreover a modified lyapunov krasovskii function lkf is constructed combining ito s differential formula and free weighting matrix method less conservative results are presented in terms of the linear matrix inequality lmi furthermore an observer based non fragile asynchronous h controller is designed without any limits on the system parameters finally three numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed results

a viability theorem for set valued states in a hilbert space abstract applications in robust control problems and shape evolution motivate the mathematical interest in control problems whose states are compact possibly non convex sets rather than vectors this leads to evolutions in a basic set which can be supplied with a metric like the well established pompeiu hausdorff distance but it does not have an obvious linear structure this article extends differential inclusions with state constraints to compact valued states in a separable hilbert space h the focus is on sufficient conditions such that a given constraint set of compact subsets is viable a k a weakly invariant our main result extends the tangential criterion in the well known viability theorem usually for differential inclusions in a vector space to the metric space of non empty compact subsets of h

technical communique stabilization of a class of uncertain large scale stochastic systems with time delays this paper focuses on a class of large scale interconnected bilinear stochastic systems with time delays and time varying parameter uncertainties the problem we address is to design a robust decentralized controller such that the closed loop interconnected stochastic system is globally asymptotically stable in probability for all admissible uncertainties and time delays first robust stability analysis is given in terms of a set of linear matrix inequalities lmis then it is shown that the robust decentralized stabilization can be solved by an lmi based design method

h control of discrete time linear systems with norm bounded uncertainties and time delay in state this paper deals with h control problem for discrete time linear systems with norm bounded uncertainties and time delay in state in terms of a modified riccati inequality for discrete time linear systems a sufficient condition is presented and a state feedback control law is also given the proposed control law is a memoryless state feedback control law

consensus tracking for higher order multi agent systems with switching directed topologies and occasionally missing control inputs abstract this paper studies the distributed consensus tracking problem of linear higher order multi agent systems with switching directed topologies and occasionally missing control inputs in this framework the underlying topology of dynamic agents may switch among several directed graphs each having a directed spanning tree rooted at the leader furthermore the control inputs to the followers may be temporally missed due to actuator failures and network induced packet loss to guarantee asymptotic consensus tracking in such a multi agent system several distributed controllers are constructed based only on the relative state information of neighboring agents by appropriately constructing a switching lyapunov function and using tools from the m matrix theory some sufficient conditions for achieving distributed consensus tracking are provided finally some numerical simulations are given to illustrate the theoretical analysis

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

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

novel delay dependent master slave synchronization criteria of chaotic lur e systems with time varying delay feedback control this paper is concerned with the issue of master slave synchronization for chaotic lur e systems clss with time varying delay feedback control a novel integral inequality is developed by employing two adjustable parameters which encompasses the celebrated wirtinger s integral inequality and jensen s inequality as two special cases by constructing an augmented lyapunov krasovskii functional lkf taking fully the information time varying delay range into account less conservative delay dependent synchronization criteria are established in the form of linear matrix inequalities lims besides the desired controller gain can be achieved by introducing new nonlinear function conditions which have not been proposed so far finally a numerical example of typical chua s circuit is presented to show the improvements over the existing criteria and the effectiveness of the design approach

indefinite derivative lyapunov krasovskii functional method for input to state stability of nonlinear systems with time delay in this paper the problem of the input to state stability iss for nonlinear systems with time delay is investigated a continuously differentiable lyapunov krasovskii functional with indefinite derivative is introduced to derive the iss of the systems which generalizes the classic lyapunov krasovskii functional with positive definite derivative as a result the uniform stability and uniform asymptotic stability criteria of nonlinear systems with time delay are also established by employing the proposed lyapunov krasovskii functional

on the solution of stochastic differential inclusion abstract in the paper the problem of existence and uniqueness of the solution of the stochastic differential inclusion dx t f t x db t g t x dt is investigated under some assumption of the dissipativity type on f and g

robust h filter design for neutral stochastic uncertain systems with time varying delay abstract in this paper the robust h filtering problem for a class of neutral stochastic systems is discussed the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delay the parameter uncertainties are assumed to be time varying norm bounded using the stochastic lyapunov stability theory and ito s differential rule a full order filter is designed for all admissible uncertainties and time varying delay which is expressed in the form of linear matrix inequality lmi the dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable while achieving a prescribed stochastic robust h performance level at the end of this paper a numerical example is given to demonstrate the usefulness of the proposed method

set valued and fuzzy stochastic differential equations driven by semimartingales abstract in the paper we present set valued and fuzzy stochastic integrals with respect to semimartingale integrators as well as their main properties then we study the existence of solutions to set valued and fuzzy set valued stochastic differential equations driven by semimartingales the stability of solutions is also established

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

duality and uniqueness of convex solutions to stationary hamilton jacobi equations value functions for convex optimal control problems on infinite time intervals are studied in the framework of duality hamilton jacobi characterizations and the conjugacy of primal and dual value functions are of main interest close ties between the uniqueness of convex solutions to a hamilton jacobi equation the uniqueness of such solutions to a dual hamilton jacobi equation and the conjugacy of primal and dual value functions are displayed simultaneous approximation of primal and dual infinite horizon problems with a pair of dual problems on finite horizon for which the value functions are conjugate leads to sufficient conditions on the conjugacy of the infinite time horizon value functions consequently uniqueness results for the hamilton jacobi equation are established little regularity is assumed on the cost functions in the control problems correspondingly the hamiltonians need not display any strict convexity and may have several saddle points

improved delay dependent stabilization for a class of networked control systems with nonlinear perturbations and two delay components abstract this paper focuses on the problem of delay dependent state feedback control for a class of networked control systems ncss with nonlinear perturbations and two delay components based on the dynamic delay interval ddi method and the wirtinger integral inequality some improved delay dependent stability analysis are obtained furthermore the results are extended to the conditions of ncss with one time delay and the corresponding stability analysis results and state feedback controller are obtained finally some numerical examples and simulations are given to show the effectiveness of the proposed methods

weak solutions of set valued stochastic differential equations abstract the paper is devoted to the existence of weak solutions of set valued stochastic differential equations such equations were considered in the authors paper 22 where existence and uniqueness of strong solutions have been investigated now apart from the existence of weak solutions the weak compactness in distribution of the set of all weak solutions of set valued stochastic differential equations is considered

the interrelation between stochastic differential inclusions and set valued stochastic differential equations abstract in this paper we connect the well established theory of stochastic differential inclusions with a new theory of set valued stochastic differential equations solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty bounded convex and closed subsets of the space l 2 consisting of square integrable random vectors we show that for the solution x to a set valued stochastic differential equation corresponding to a stochastic differential inclusion there exists a solution x for this inclusion that is a l 2 continuous selection of x this result enables us to draw inferences about the reachable sets of solutions for stochastic differential inclusions as well as to consider the viability problem for stochastic differential inclusions

remarks on unboundedness of set valued ito stochastic integrals abstract the paper deals with set valued stochastic integrals which are defined as a random multifunctions integrable boundedness of a such integral is one of the most important features in potential applications unfortunately up to now there were no correct proofs of such property surprisingly also a negative answer to this problem is still not explained correctly hence the problem seems to be still undetermined we shall show that in general the answer is negative we shall provide several relatively simple examples both in convex and nonconvex valued case as a consequence we will show that under some restrictions on the class of selections of the integrand the integrable boundedness of set valued ito s integral is equivalent to its single valuedness

state feedback control of systems with multiplicative noise via linear matrix inequalities we consider lti systems perturbed by parametric uncertainties modeled as white noise disturbances we show how to maximize via state feedback control the smallest norm of the noise intensity vector producing instability in the mean square sense using convex optimization over linear matrix inequalities we also show how to maximize performance robustness where performance is measured by expected output energy with either bounded initial conditions and zero inputs classical lqg cost or zero initial conditions and deterministic inputs of bounded energy a generalization of the h norm

robust fuzzy control for uncertain stochastic time delay takagi sugeno fuzzy models for achieving passivity this paper focuses on the robust passive stability and stabilization problems for uncertain nonlinear stochastic time delay systems via the fuzzy modeling approach the nonlinear stochastic system is described by takagi sugeno t s fuzzy model in which the consequent parts are presented by linear stochastic time delay differential equation with lyapunov krasovskii function and improved jensen s inequality the stability criteria are derived in addition the passivity theory is employed to discuss external disturbance effect on system for achieving attenuation performance according to the proposed design method the fuzzy controller is carried out by parallel distributed compensation pdc concept to guarantee the robust asymptotical stability and attenuation performance of system in the sense of mean square finally a synchronous generator power system is presented to manifest the application and effectiveness of the proposed fuzzy control method

on random fuzzy differential equations we consider a cauchy problem in a random fuzzy setting under the condition of lipschitzean right hand side the existence and uniqueness of the solution is proven also the continuous dependence on the right hand side and initial condition is shown some kind of boundedness of the solution is established

nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled data control this paper considers nonfragile exponential synchronization for complex dynamical networks cdns with time varying coupling delay the sampled data feedback control which is assumed to allow norm bounded uncertainty and involves a constant signal transmission delay is constructed for the first time in this paper by constructing a suitable augmented lyapunov function and with the help of introduced integral inequalities and employing the convex combination technique a sufficient condition is developed such that the nonfragile exponential stability of the error system is guaranteed as a result for the case of sampled data control free of norm bound uncertainties some sufficient conditions of sampled data synchronization criteria for the cdns with time varying coupling delay are presented as the formulations are in the framework of linear matrix inequality these conditions can be easily solved and implemented two illustrative examples are presented to demonstrate the effectiveness and merits of the proposed feedback control

robust stability and stabilization of linear stochastic systems with markovian switching and uncertain transition rates abstract this paper is concerned with the robust stabilization problem for a class of linear uncertain stochastic systems with markovian switching the uncertain stochastic system with markovian switching under consideration involves parameter uncertainties both in the system matrices and in the mode transition rates matrix new criteria for testing the robust stability of such systems are established in terms of bi linear matrix inequalities blmis and sufficient conditions are proposed for the design of robust state feedback controllers a numerical example is given to illustrate the effectiveness of our results

a class of stochastic differential equations with expectations in the coefficients this paper considers a class of nonlocal stochastic differential equations with time varying delay whose coefficients are dependent on expectations by applying the m matrix technique the existence and uniqueness of the global solution of nonlocal stochastic differential delay equations is studied a class of moment estimates of solutions is also considered the results improve our previous work hu and huang 2012 1 an example is provided to illustrate the effectiveness of our results

set valued stochastic integral equations driven by martingales abstract we consider a notion of set valued stochastic lebesgue stieltjes trajectory integral and a notion of set valued stochastic trajectory integral with respect to martingale then we use these integrals in a formulation of set valued stochastic integral equations the existence and uniqueness of the solution to such the equations is proven as a generalization of set valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales

brief paper a delay decomposition approach to l2 l filter design for stochastic systems with time varying delay this paper investigates the problem of l 2 l filter design for a class of stochastic systems with time varying delay the addressed problem is the design of a full order linear filter such that the error system is asymptotically mean square stable and a prescribed l 2 l performance is satisfied in order to develop a less conservative filter design a new lyapunov krasovskii functional lkf is constructed by decomposing the delay interval into multiple equidistant subintervals and a new integral inequality is established in the stochastic setting then based on the lkf and integral inequality the delay dependent conditions for the existence of l 2 l filters are obtained in terms of linear matrix inequalities lmis the resulting filters can ensure that the error system is asymptotically mean square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances finally two examples are given to illustrate the effectiveness of the proposed method

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

robust stability of uncertain fuzzy bam neural networks of neutral type with markovian jumping parameters and impulses abstract in this paper the problem of neutral type impulsive bidirectional associative memory neural networks nibamnns with time delays are first established by a takagi sugeno t s fuzzy model in which the consequent parts are composed of a set of nibamnns with interval delays and markovian jumping parameters mjps sufficient conditions to check the robust exponential stability of the derived model are based on the lyapunov krasovskii functionals lkfs containing some novel triple integral terms lyapunov stability theory and employing the free weighting matrix method the delay dependent stability conditions are established in terms of linear matrix inequalities lmis which can be very efficiently solved using matlab lmi control toolbox finally numerical examples and remarks are given to illustrate the effectiveness and usefulness of the derived results

state feedback stabilization for stochastic feedforward nonlinear systems with time varying delay this paper investigates a class of stochastic feedforward nonlinear systems with time varying delay by introducing the homogeneous domination approach to stochastic systems a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

brief paper almost sure exponential stabilisation of stochastic systems by state feedback control so far a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean square stability this paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean square sense the results are expressed in terms of linear matrix inequalities lmis which are easy to be checked in practice by using matlab toolbox moreover the control structure in this paper appears not only in the drift part but also in the diffusion part of the underlying stochastic system

exponential stability of stochastic delay interval systems abstract although deterministic interval systems have received a great deal of attention so far there is no work on stochastic interval systems the main aim of this paper is to initiate the study of stochastic interval systems of course there are many properties of such systems to be investigated but this paper will concentrate on the study of exponential stability of stochastic interval systems with time varying delays the main technique used in this paper is the razumikhin type theorem established recently by mao stochastic process appl 65 1996 233 250

robust h control for linear time invariant systems with norm bounded uncertainty in the input matrix abstract this paper focuses on the problem of robust h control design for a class of linear time invariant systems with uncertainty in the state space model we consider uncertain systems with norm bounded parameter uncertainty in the input matrix the paper presents a state feedback control design which stabilizes the plant for all admissible uncertainties and also guarantees an h norm bound constraint on disturbance attenuation paralleling to the theory of robust control the robust h control problem is solved via the notion of quadratic stabilization with an h norm bound constraint necessary and sufficient conditions for quadratic stabilization with an h norm bound are derived it is shown that the solution to this problem involves solving a parameter dependent algebraic riccati equation the results can be regarded as extensions of existing results on robust stabilization of linear uncertain systems and h optimal control

approximation schemes for fuzzy stochastic integral equations we consider fuzzy stochastic integral equations with stochastic lebesgue trajectory integrals and fuzzy stochastic ito trajectory integrals some methods of construction of approximate solutions to such the equations are examined we study the picard type approximations the caratheodory type approximations and the maruyama type approximations of solutions in considered framework the solutions and approximate solutions are mappings with values in the space of fuzzy sets with basis of square integrable random vectors under lipschitz and linear growth conditions each sequence of considered approximate solutions converges to the exact unique solution of the given fuzzy stochastic integral equation for each type of approximate solutions we show that the sequence of approximations is uniformly bounded and obtain some bounds for a distance between nth approximation and exact solution

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

robust reduced order h output feedback control of retarded stochastic linear systems a method for designing reduced order output feedback controllers for linear time invariant retarded systems with state multiplicative wiener type noise is introduced which achieves a minimum bound on the h performance level a cost function is defined that is the expected value of the standard h performance cost with respect to the stochastic parameters a solution is thus obtained for the reduced order h output feedback control problem for the stationary case via the input output approach where the system is replaced by a non retarded one that contains deterministic norm bounded uncertainties the results achieved for the nominal case are extended to the uncertain case where the system matrices reside in a given polytope a numerical example taken from the field of aircraft control is given that demonstrates the applicability of the theory developed

martingale problem to stratonovich stochastic inclusion abstract in the paper we consider a martingale problem approach to stratonovich stochastic inclusion the proposed method enables us to investigate both the existence and topological properties of the set of weak solutions to such inclusions

diffusion equation for multivalued stochastic differential equations abstract deterministic oscillations with bilinear hysteresis are governed by a multivalued differential equation of the type k b g where k is maximal monotonic and b is lipschitzian an existence and uniqueness result is proven for corresponding stochastic equation the diffusion equation satisfied by the laws of t is established in the particular case k 0 this equation is equivalent to the fokker planck equation

adaptive neural tracking control for stochastic nonlinear strict feedback systems with unknown input saturation in this paper the problem of adaptive neural tracking control is considered for a class of single input single output siso strict feedback stochastic nonlinear systems with input saturation to deal with the non smooth input saturation nonlinearity a smooth nonaffine function of the control input signal is used to approximate the input saturation function classical adaptive technique and backstepping are used for control synthesis based on the mean value theorem a novel adaptive neural control scheme is systematically derived without requiring the prior knowledge of bound of input saturation it is shown that under the action of the proposed adaptive controller all the signals of the closed loop system remain bounded in probability and the tracking error converges to a small neighborhood around the origin in the sense of mean quartic value two simulation examples are provided to demonstrate the effectiveness of the presented results

existence theorems for solutions to random fuzzy differential equations abstract we examine a random fuzzy initial value problem with two kinds of fuzzy derivatives for both cases we establish the results of existence and uniqueness of local solutions to random fuzzy differential equations the existence of global solutions is also obtained

properties of set valued integrals and set valued stochastic equations driven by two parameter martingales abstract in the paper we study properties of aumann s stochastic integral driven by a two parameter increasing process and set valued ito s integral with respect to the two parameter martingale both types of integrals are understood as set valued processes next the existence uniqueness and convergence properties of solutions to set valued stochastic integral equations with respect to such integrators are investigated we present new types of such equations that generalize those studied earlier the results obtained in the paper present a set valued counterpart dealing with this topic known both in single valued deterministic and stochastic cases

delay dependent stabilization for stochastic fuzzy systems with time delays this paper is concerned with the delay dependent stabilization problem for a class of time delay stochastic fuzzy systems the time delays are assumed to appear in both the state and the control input the purpose is the design of a state feedback fuzzy controller such that the resulting closed loop system is asymptotically stable in the mean square a delay dependent condition for the solvability of this problem is obtained in terms of relaxed linear matrix inequalities lmis by solving these lmis a desired controller can be obtained finally a numerical example is given to demonstrate the effectiveness of the present results

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

technical communique h state feedback control for generalized continuous discrete time delay system in this paper we consider the problem of designing h state feedback controller for the generalized time delay systems with delayed states and control inputs in continuous and discrete time cases respectively the generalized time delay system problems are solved on the basis of linear matrix inequality lmi technique considering time delays the sufficient condition for the existence of controller and h state feedback controller design methods are presented also using some changes of variables and schur complements the obtained sufficient condition can be rewritten as an lmi form in terms of transformed variables the proposed controller design method can be extended into the problem of robust h state feedback controller design method easily

robust stability criterion for uncertain stochastic systems with time varying delay via sliding mode control abstract this paper is focused on sliding mode control smc for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and stochastic perturbations may appear in the controlled system a new integral type switching surface function is first constructed then a sufficient condition for the existence of sliding surface is established in terms of linear matrix inequalities lmis by employing some free weighting matrices which guarantees the robustly stochastically stable of the sliding mode dynamic system with time varying delay for all admissible uncertainties moreover a smc law is synthesized to drive the system state trajectories onto the predefined switching surface in a finite time finally a simulation example is provided to illustrate the effectiveness of the proposed theory

bolza problems with discontinuous lagrangians and lipschitz continuity of the value function we study the local lipschitz continuity of the value function v associated with a bolza problem in the presence of a lagrangian l x q convex and uniformly superlinear in q but only borel measurable in x under these assumptions the associated integral functional is not lower semicontinuous with respect to the suitable topology which ensures the existence of minimizers so all results known in the literature fail to apply yet the lipschitz regularity of v does not depend on the existence of minimizers in fact it is enough to control the derivatives of quasi minimal curves but the problem is nontrivial due to the general growth conditions assumed here on l x cdot we propose a new approach based on suitable reparameterization arguments to obtain suitable a priori estimates on the lipschitz constants of quasi minimizers as a consequence of our analysis we derive the lipschitz continuity of v and a compactness result for value functions associated with sequences of locally equibounded discontinuous lagrangians

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

on connections between stochastic differential inclusions and set valued stochastic differential equations driven by semimartingales abstract in the paper we study properties of solutions to stochastic differential inclusions and set valued stochastic differential equations with respect to semimartingale integrators we present new connections between their solutions in particular we show that attainable sets of solutions to stochastic inclusions are subsets of values of multivalued solutions of certain set valued stochastic equations we also show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set valued stochastic equation the results obtained in the paper generalize results dealing with this topic known both in deterministic and stochastic cases

improved delay dependent robust stability criteria for uncertain time delay systems abstract this paper deals with the robust stability analysis for uncertain systems with time varying delay new delay dependent robust stability criteria of uncertain time delay systems are proposed by exploiting appropriate lyapunov functional candidate these developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism due to the introduction of a method to estimate the upper bound of the derivative of lyapunov functional candidate without ignoring the additional useful terms numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method

robust h state feedback control for linear systems with state delay and parameter uncertainty this paper addresses the problem of robust h state feedback control design for linear systems with state delay and parameter uncertainty based on a positive definite solution of a modified algebraic riccati equation the proposed robust h static state feedback controller stabilizes uncertain time delay systems independently of delays and guarantees an h norm bound constraint on disturbance attenuation for all admissible uncertainties furthermore it is shown that no advantage can be obtained from the use of a proper linear dynamic state feedback compared with the use of static state feedback illustrative examples are given to demonstrate the applicability of the proposed approach

ito type stochastic fuzzy differential equations with delay abstract in the paper we give some foundations for the studies of stochastic fuzzy delayed differential equations we prove the existence and uniqueness of solutions to such the equations to obtain our result we assume that the coefficients of the equation satisfy the lipschitz condition together with linear growth condition we estimate the distance between approximate solution and exact solution also the stability of solution with respect to the initial history is shown an application of stochastic fuzzy delayed differential equations in the modeling of population growth is indicated

robust h control for linear discrete time systems with norm bounded time varying uncertainty the problem of robust h analysis and synthesis for linear discrete time systems with norm bounded time varying uncertainty is studied in this paper it will be shown that this problem is equivalent to the problem of h analysis and synthesis of an auxiliary system the necessary and sufficient conditions for the equivalency are proved thus the original problem can be solved by existing h control methods

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

the guaranteed cost control for uncertain nonlinear large scale stochastic systems via state and static output feedback abstract the guaranteed cost control gcc problem involved in decentralized robust control of a class of uncertain nonlinear large scale stochastic systems with high order interconnections is considered after determining the appropriate conditions for the stochastic gcc controller a class of decentralized local state feedback controllers is derived using the linear matrix inequality lmi the extension of the result of the study to the static output feedback control problem is discussed by considering the karush kuhn tucker kkt conditions the efficiency of the proposed design method is demonstrated on the basis of simulation results

some properties of strong solutions to stochastic fuzzy differential equations we consider stochastic fuzzy differential equations driven by m dimensional brownian motion such equations can be useful in modeling of hybrid dynamic systems where the phenomena are subjected to two kinds of uncertainties randomness and fuzziness simultaneously under a boundedness condition which is weaker than linear growth condition and the lipschitz condition we obtain existence and uniqueness of solution to stochastic fuzzy differential equations solutions which are fuzzy stochastic processes and their uniqueness are considered to be in a strong sense an estimation of error of the picard approximate solution is established we give a boundedness type result for the solution defined on finite time interval also the stabilities of solution on initial condition and coefficients of the equation are shown the existence and uniqueness of a solution defined on infinite time interval is proven finally some applications of fuzzy stochastic differential equations are considered all the results presented in this paper apply to set valued stochastic differential equations

set membership identification of switched linear systems with known number of subsystems this paper addresses the problem of robust identification of a class of discrete time linear hybrid systems switched linear models in a set membership framework given a finite collection of input output data from a noisy process the objective is twofold i establish whether this data was generated by a system that switches amongst an a priori known number of subsystems and ii in that case identify a suitable set of linear models along with a switching sequence that can explain the available experimental information our main result shows that these problems are equivalent to minimizing the rank of a matrix whose entries are affine in the optimization variables subject to a convex constraint imposing that these variables are the moments of an unknown borel measure with finite support the use of well known tight convex relaxations of rank allows for further reducing the problem to a semidefinite optimization that can be efficiently solved in the second part of the paper we extend these results to handle sensor failures that result in corrupted input output measurements assuming that these failures are infrequent we show that the problem can be recast into an optimization form where the objective is to simultaneously minimize the rank of a matrix and the number of nonzero rows of a second one in both cases appealing to well known convex relaxations of rank and sparsity leads to overall semidefinite optimization problems that can be efficiently solved these results are illustrated with multiple examples showing substantially improved identification performance in the presence of noise and sensor faults

quantized feedback fuzzy sliding mode control design via memory based strategy this paper is concerned with the sliding mode control smc design for a class of takagi sugeno t s fuzzy nonlinear systems subject to model uncertainties and input quantization mismatch a novel memory based sliding surface is presented which includes not only the current states but also the past state information of the systems sufficient conditions for the design of the switching gains are given via linear matrix inequality lmi technique and then the reaching conditions of the sliding surface is constructed to ensure the reachability of the sliding manifold furthermore an adaptive neuro fuzzy inference system anfis is introduced for reducing the high frequency chattering induced by the signum function term in the sliding mode control the effectiveness of the proposed methodology is illustrated by matlab simulations

stochastic representation of partial differential inclusions abstract partial differential inclusions of the form u t l f g u c u and l fg u c u where l fg is a uniformly parabolic second order set valued operator are considered in particular basing on diffusions properties of weak solutions to stochastic differential inclusions some existence and representation theorems for solutions of such type partial differential inclusions are given

robust stability of uncertain stochastic differential delay equations in this paper we first discuss the robust stability of uncertain linear stochastic differential delay equations we then extend the theory to cope with the robust stability of uncertain semi linear stochastic differential delay equations we shall also give several examples to illustrate our theory

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

some properties of set valued stochastic integrals abstract the present paper is devoted to properties of set valued stochastic integrals defined as some special type of set valued random variables in particular it is shown that if the probability base is separable or probability measure is nonatomic then defined set valued stochastic integrals can be represented by a sequence of ito s integrals of nonanticipative selectors of integrated set valued processes immediately from michael s continuous selection theorem it follows that the indefinite set valued stochastic integrals possess some continuous selections the problem of integrably boundedness of set valued stochastic integrals is considered some remarks dealing with stochastic differential inclusions are also given

lower semicontinuous solutions of hamilton jacobi bellman equations the value function of mayer s problem arising in optimal control is investigated and lower semicontinuous solutions of the associated hamilton jacobi bellman equation are defined in three equivalent ways under quite weak assumptions about the control system the value function is the unique solution moreover it is stable with respect to perturbations of the control system and the cost it coincides with the viscosity solution whenever it is continuous

robust decentralized stabilization of markovian jump large scale systems a neighboring mode dependent control approach abstract this paper is concerned with the decentralized stabilization problem for a class of uncertain large scale systems with markovian jump parameters the controllers use local subsystem states and neighboring mode information to generate local control inputs a sufficient condition involving rank constrained linear matrix inequalities is proposed for the design of such controllers a numerical example is given to illustrate the developed theory

delay dependent l2 l filter design for stochastic time delay systems abstract this paper is concerned with the problem of l 2 l filter design for a class of stochastic time delay systems a delay dependent sufficient condition is presented which guarantees the existence of a linear filter ensuring that the filtering error system is stochastically asymptotically stable and its l 2 l performance satisfies a prescribed level a desired filter can be constructed by solving certain linear matrix inequalities a numerical example is given to demonstrate the effectiveness of the proposed method

exponential stability on stochastic neural networks with discrete interval and distributed delays this brief addresses the stability analysis problem for stochastic neural networks snns with discrete interval and distributed time varying delays the interval time varying delay is assumed to satisfy 0 d1 d t d2 and is described as d t d 1 h t with 0 h t d 2 d 1 based on the idea of partitioning the lower bound d 1 new delay dependent stability criteria are presented by constructing a novel lyapunov krasovskii functional which can guarantee the new stability conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis numerical examples are provided to illustrate the effectiveness and less conservatism of the developed results

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

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

robust h control for uncertain discrete time systems with circular pole constraints this paper investigates the problem of robust h control for uncertain discrete time systems with circular pole constraints the system under consideration is subject to norm bounded time invariant uncertainties in both the state and input matrices the problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region and the h norm of the closed loop transfer function is strictly less than a given positive scalar for all admissible uncertainties by introducing the notion of quadratic d stabilizability with an h norm bound the problem is solved necessary and sufficient conditions for quadratic d stabilizability with an h norm bound are derived our results can be regarded as extensions of existing results on robust h control and robust pole assignment of uncertain systems

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

robust h sub spl infin compensator design for time delay systems with norm bounded time varying uncertainties considers robust h sub spl infin compensator design for linear systems that involve unknown time delays both in states and controls and time varying norm bounded parameter uncertainties sufficient conditions for designing robust compensators are obtained in terms of two riccati inequalities which are not mutually coupled through which a full order robust h sub spl infin compensator can be obtained finally a small example is given to show the applicability of the proposed approach

h tracking of uncertain stochastic time delay systems the problem of state robust h tracking control for uncertain stochastic systems with interval time varying delay is considered in this paper the target is to design a memory state feedback controller such that the resulting closed loop augmented system is robustly stochastically asymptotically stable and the states of original systems can follow the reference signal with given h performance firstly by constructing delay partitioning dependent lyapunov krasovskii functional with reciprocally convex approach a delay dependent condition guaranteeing the robust h tracking performance is proposed in a set of matrix inequalities secondly new stability criteria for stochastic systems with time varying delay are given with less conservativeness than some recent results thirdly memory state feedback controller is designed via a set of linear matrix inequalities lmis which can be solved by matlab lmi toolbox at last numerical simulations are addressed to show the effectiveness of the proposed methods

extended hamilton jacobi characterization of value functions in optimal control this paper examines generalized solutions to the hamilton jacobi equation the hamiltonian h t x p is assumed convex in p but is not constrained to have linear growth in this variable this corresponds to a certain class of generalized bolza problems related to optimal control lower semicontinuous solutions are considered and it is shown that there is a unique solution the so called value function of the underlying bolza problem in proving the main result we use recent improved necessary optimality conditions viability is also used in a new way in connection to differential inclusions with unbounded images