The Research On Stochastic Stabilization Of Markovian Jumping Neutral Systems With Time-delays

It is well known that many physical systems are subject to frequent unpredictable structural changes,such as random failures,repairs of components,sudden environment disturbances,abrupt variation of the operating point on a nonlinear plant,etc.Markovian jump systems are often used to describe such systems.Generally speaking,a Markovian jump system is a hybrid system with state vector that has two components x(t)and r(t),where x(t)denotes the state and r(t)is a continuous-time Markov chain,which is usually regarded as the mode.In its operation,the jump system will switch from one mode to another in a random way,which is determined by a continuous-time Markov chain r(t),based on a Markov chain with finite state space S =(1,2,...,s).Therefore,it is important to research the dynamics behaviors of systems with Markovian jumping parameters.On the other hand,neutral functional differential equations are often used to describe some practical engineering systems,such as computer aided design,circuit analysis,real time simulation of mechanical systems,chemical process simulation,power systems,population dynamics,automatic control and so on.In the process of operating or transmitting signals of these practical systems,Markovian jump and neutral delay often appear,so these practical systems are often modeled by Markovian jumping neutral systems modelling to be precisely characterize its dynamic characteristics.Hence,by constructing suitable Lyapunov functional,combining LMI technique and the free-weight matrix approach,some inequalities bounded skills(Jensen inequality,the free-matrix-based integral inequality,reciprocally convex combination inequalities),and flexibly using It?'s differential formula,LaShall-type invariance principle,martingale theory and other stochastic analysis techniques.This paper focuses on the stability and stabilization of two kinds of Markovian jumping neutral systems.And the main research contents include four aspects:(1)The problems of stability and stabilization for neutral systems with both Markovian jumping parameters and time-varying delay are discussed.By the correlative methods,the stochastic stability and stabilization criteria of Markovian jumping neutral systems with time-varying delay are given in terms of LMIs.(2)The issues of stability and stabilization for a class of stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays are considered.By using the semi-martingale convergence theorem,sufficient conditions of the globally exponential stability in mean square and almost surely exponential stability are established.On the basis of these stability consitions,the controller design and analysis of this system is discussed and the relevant stabilization conditions are obtained.(3)The problem of the almost surely asymptotic synchronization for a class of stochastic neural networks of neutral type with both Markovian jumping parameters and mixed time delays are studied.Based on the stochastic analysis theory,LaShall-type invariance principle of stochastic differential delay equations and delayed state feedback control technique,some novel delay-dependent sufficient criteria to guarantee the almost surely asymptotic synchronization are given.(4)The problems of exponential passivity and passivity control on neutral stochastic neural networks with leakage delay and partially unknown transition probabilities in Markovian jump are analyzed.Based on some related theories,sufficient conditions for delay-dependent exponential passivity and stochastic passivity stabilization are obtained.