stochastic stability and robust control for sampled data systems with markovian jump parameters in this paper the problems of stochastic stability and robust control for a class of uncertain sampled data systems are studied the systems consist of random jumping parameters described by finite state semi markov process sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented the conditions for the existence of a sampled data feedback control and a multirate sampled data optimal control for the continuous time uncertain markovian jump systems are also obtained the design procedure for robust multirate sampled data control is formulated as linear matrix inequalities lmis which can be solved efficiently by available software toolboxes finally a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques

robust h sup spl infin filtering for uncertain markovian jump systems with mode dependent time delays this paper considers the problem of robust h sup spl infin filtering for uncertain markovian jump linear systems with time delays which are time varying and depend on the system mode the parameter uncertainties are time varying norm bounded the aim of this problem is to design a markovian jump linear filter that ensures robust exponential mean square stability of the filtering error system and a prescribed l sub 2 induced gain from the noise signals to the estimation error for all admissible uncertainties a sufficient condition for the solvability of this problem is obtained the desired filter can be constructed by solving a set of linear matrix inequalities an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

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

h control for markovian jump systems with partially unknown transition rates via an adaptive method abstract this paper investigates the problem of the h control for a class of continuous time markovian jump systems with partially unknown transition rates an adaptive h performance index is defined to describe the disturbance attenuation performance of markovian jump systems by combining the linear matrix inequality lmi approach for designing h controllers and the adaptive method for estimating the unknown terms a new method for designing the h controllers is proposed where an estimation of the transition rate matrix is given and the controller parameter matrices are dependent on the known transition rates and the estimations of the unknown terms the sufficient conditions for the existence of the adaptive state feedback controller and the adaptive dynamic output feedback controller are proposed and the estimations of the unknown transition rates are obtained from the adaptive laws it is shown that the proposed adaptive controllers provide better performance than the traditional fixed gain controllers a practical example is provided to illustrate the effectiveness and advantage of the proposed method

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

non fragile control design for interval valued fuzzy systems against nonlinear actuator faults abstract in this paper we consider the reliable non fragile h control design problem for a class of discrete time interval valued fuzzy systems with actuator faults more precisely the actuator fault model considered in the controller design consists of linear and nonlinear fault terms the main focus of this paper is to design a non fragile state feedback controller that is characterized by membership functions described by upper and lower membership functions and nonlinear weighting functions it should be mentioned that the proposed interval valued fuzzy system and the controller do not share same membership functions a novel set of sufficient conditions is obtained by transforming the controller design problem into a multi objective convex optimization problem based on the linear matrix inequality and the lyapunov functional approaches which ensures the robust asymptotic stability of the addressed system with a desired h performance index finally two numerical examples including an application oriented model mass spring damping system are presented to demonstrate the effectiveness of the proposed design technique

technical communique norm invariant discretization for sampled data fault detection in this paper the problem of fault detection in sampled data systems is studied it is shown that norms of a sampled system are equal to the corresponding norms of a certain discrete time system based on this discretization the sampled data fault detection problem can be converted to an equivalent discrete time problem a framework that unifies the h 2 and h optimal residual generators in sampled data systems is then proposed

event triggered non fragile control for linear systems with actuator saturation and disturbances abstract this paper investigates the problem of event triggered non fragile dynamic output feedback controller design for linear systems with actuator saturation and disturbances the controller to be designed is supposed to include additive gain variations by using lyapunov stability theory and adding slack matrix variables new sufficient conditions are derived to design the event triggered parameters and the controller gains compared with the existing non fragile dynamic output feedback controller design methods the structural restriction on the lyapunov matrix is relaxed the effectiveness of the proposed method is demonstrated by two examples

brief paper passivity based sliding mode control of uncertain singular time delay systems in this paper the problem of sliding mode control smc with passivity of a class of uncertain nonlinear singular time delay systems is studied an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order uncertain singular time delay system by introducing some slack matrices a delay dependent sufficient condition is proposed in terms of linear matrix inequality lmi which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive the passification solvability condition is then established moreover a smc law and an adaptive smc law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed theory

delay dependent sampled data control based on delay estimates in this paper the sampled data stabilization of linear time invariant systems with feedback delay is considered we assume that the delay is time varying and that its value is approximatively known we investigate how to use the available information about the evolution of delays for adapting the control law in real time numerical methods for the design of a delay dependent controller are presented this allows for providing a control for some cases in which the stabilization cannot be ensured using a controller with a fixed structure

non fragile exponential stability assignment of discrete time linear systems with missing data in actuators this technical note is concerned with the non fragile exponential stabilization for a class of discrete time linear systems with missing data in actuators the process of missing data is modeled by a discrete time markov chain with two state components when no uncertainty exists in the controllers a necessary and sufficient condition which not only guarantees the exponential stability but also gives a lower bound on the decay rate is established in terms of linear matrix inequalities lmis based on this condition an lmi based approach is provided to design a non fragile state feedback controller such that the closed loop system is exponentially stable with a prescribed lower bound on the decay rate for the known missing data process and all admissible uncertainties in controllers a numerical example is provided to show the effectiveness of the theoretical results

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

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

h filtering for nonuniformly sampled systems a markovian jump systems approach abstract this paper is concerned with the design of an h filter for a sampled data system where the measurement is sampled nonuniformly and randomly but the input is updated uniformly at a fast rate the process of nonuniform measurement sampling is modeled using a markov chain therefore the discrete time system together with the markov chain is a markovian jump system a mode dependent full order h filter is constructed sufficient lmi conditions are derived to ensure stochastic stability and h disturbance attenuation for the error system the case of unknown measurement sampling probabilities is also considered finally the effectiveness of the proposed approach is demonstrated through simulation results and a comparison with a general time varying h filter

possibilities as cumulative subjective probabilities and a norm on the space of congruence classes of fuzzy numbers motivated by an expected utility functional abstract in our prior paper jamison and lodwick 1996 we defined a fuzzy function and discussed the theory for optimizing unconstrained fuzzy functions in that paper we described the need for a measure for comparing different possibility distributions in order to determine the decision makers preference for one distribution over another in this paper we develop one such measure we begin by developing possibility distributions from a set of axioms to show that possibility levels can be viewed as cumulative subjective probabilities we use this development to motivate a norm on the vector space of congruence classes of fuzzy numbers this norm is based on an expected utility functional we show that our normed space is complete if the supports of our fuzzy numbers are contained within a bounded subset of the real line

reconstruction of continuous time systems from their non uniformly sampled discrete time systems a continuous time system cannot be recovered solely from its uniformly sampled discrete time model through the zero order hold discretization or step invariant transformation but our studies indicate that it can be recovered uniquely from its non uniformly sampled discrete time model in this paper we discuss some related issues of non uniformly sampled systems including model derivation controllability and observability computation of single rate models with different sampling periods reconstruction of continuous time systems and parameter identification of non uniformly sampled discrete time systems a numerical example is also given for illustration

dissipativity based sliding mode control of switched stochastic systems this technical brief is concerned with dissipativity analysis and dissipativity based sliding mode control smc of continuous time switched stochastic systems firstly a sufficient condition is proposed to guarantee the mean square exponential stability and strict dissipativity for the switched stochastic system then an integral type sliding surface function is designed for establishing a sliding mode dynamics which can be formulated by a switched stochastic system with an external disturbance uncertainty dissipativity analysis and synthesis are both investigated for the sliding mode dynamics and consequently sufficient conditions are derived which pave the way for solving the dissipativity analysis and control problems moreover a smc law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time finally the efficiency of the theoretical findings is demonstrated by an illustrative example

finite time h static output control of markov jump systems with an auxiliary approach this paper considers the finite time h static output feedback control of markov jump systems with the help of introducing two new variables related to the original system state and output sufficient conditions for the closed loop system to be stochastic finite time boundedness with the prescribed h performance level are proposed in terms of linear matrix inequalities lmis meanwhile the static output control gains are solved explicitly by the proposed conditions it is shown that the proposed method is less or at least the same conservative than the existing result lastly a numerical example is given to demonstrate the effectiveness of the proposed method

robust finite time stability and stabilization of uncertain markovian jump systems with time varying delay this paper deals with the robust finite time stability and stabilization problems of uncertain stochastic delayed jump systems where the uncertainty is in the form of additive perturbations and exists in the drift and diffusion sections simultaneously though perturbation time varying delay and brownian motion existing at the same time two conditions checking its robust finite time stability are proposed by a mode dependent parameter approach which are different from some existing methods based on the proposed results sufficient conditions for the existence of the state feedback controller are provided with lmis which could be solved directly it is seen that all the features of the underlying system such as time varying delay perturbation diffusion mode dependent parameters and uncertain transition rate matrix play important roles in the system analysis and synthesis of finite time stability finally numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods

mode independent control of singular markovian jump systems in this paper the mode independent control problem of singular markovian jump systems is firstly studied by exploiting a stochastic optimization viewpoint a new kind of mode independent h controller satisfying a minimum variance approximation is constructed whose gain is composed of some mode dependent control gains the available probability of system mode is described by the bernoulli variable and taken into account it shows that such a probability plays an important role in system analysis and associates mode independent controller with mode dependent controllers when the probability is unknown a kind of adaptive controller is proposed such that the resulting closed loop system is robust stochastically admissible with an h performance all the proposed conditions are given in terms of linear matrix inequalities two numerical examples are used to demonstrate the effectiveness of the proposed methods

hyperbolic phenomena in a strongly degenerate parabolic equation we consider the equation u t u u x x where 0 and where is a strictly increasing function with lim s we solve the associated cauchy problem for an increasing initial function and discuss to what extent the solution behaves qualitatively like solutions of the first order conservation law u t u x equations of this type arise for example in the theory of phase transitions where the corresponding free energy functional has a linear growth rate with respect to the gradient

passivity based non fragile control for markovian jump systems with aperiodic sampling in this paper the problem of non fragile passive control for markovian jump systems with aperiodic sampling is investigated the considered controller is assumed to have either additive or multiplicative norm bounded uncertainties a time dependent lyapunov functional capturing the available information of the sampling pattern is constructed to derive a sufficient condition for non fragile stochastic passivity of the resultant closed loop system based on the condition a mode independent state feedback sampled data controller is designed such that for all admissible uncertainties the closed loop system is robustly stochastically passive two illustrative examples are included to demonstrate the effectiveness and merits of the proposed techniques

non fragile h control for markovian jump fuzzy systems with time varying delays abstract this paper focuses on the non fragile h control of markovian jump fuzzy systems with time varying delays in order to obtain less conservatism an improved delay partitioning method is introduced which divides the delay interval into multiple segments with a geometric sequence a modified lyapunov krasovskii functional is constructed and some less conservative delay dependent stability criteria are derived by using linear matrix inequalities technique then a non fragile controller is designed finally two numerical examples are given to show the effectiveness of the obtained results

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

input output stability of sampled data systems the authors study the l sub p input output stability of a continuous time controller using the usual arrangement of periodic sampling and zero order hold it is noted that even if the hybrid system is exponentially stable this arrangement does not yield l sub p 1

sliding mode control of markovian jump systems with incomplete information on time varying delays and transition rates this paper is concerned with robust sliding mode control smc for continuous time markovian jump delay systems with incomplete transition rates trs the time varying delays are unclear and just bounded sometimes two methods are employed to investigate this control issue one is movement decomposition method by which reduced order sliding mode dynamics is obtained the other is via sliding mode observer and full order sliding mode dynamics is obtained on the estimation space in both cases sufficient conditions are established in terms of a set of coupled linear matrix inequalities lmis to ensure the sliding mode dynamics to be mean square exponentially stable moreover novel sliding mode controllers which need not full knowledge on time varying delays are synthesized to guarantee the reachability of the prescribed sliding surface finally numerical examples are provided to illustrate the effectiveness of the proposed methods

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product

brief non fragile h control for linear systems with multiplicative controller gain variations this paper is concerned with the problem of non fragile h controller design for linear time invariant systems the controller to be designed is assumed to have multiplicative gain variations design methods are presented in terms of symmetric positive definite solutions of algebraic riccati inequalities the resulting design is such that the closed loop system is robustly stable and has an h disturbance attenuation bound with respect to the multiplicative controller gain variations a numerical example is given to illustrate the design methods