Stochastic Stability And H-infinity Control Of Descriptor Time-varying Markovian Jump Systems

Descriptor time-varying systems are a kind of widely used dynamic systems,which can accurately describe practical problems.And the descriptor time-varying Markovian jumping systems can better describe the problems while the systems are destroyed by the environment or the connection mode between subsystems is reversely changed.Therefore,the descriptor time-varying Markovian jumping systems have attracted more attention by scholars.In this thesis,the problems of the stochastic stability and the state feedback controller design against the nonlinear descriptor time-varying Markovian jump systems with partially unknown transition rates are concerned.Firstly,the nonlinear function of the system is linearized,such that the system is regular and impulse-free,and according to the existence theorem of implicit function,the conditions of the system to have one unique solution are given.Secondly,the sufficient condition of stochastic stability is established through deriving Lyapunov-Krasovskii functional combining with the relationship between transfer rates,and the state feedback controller is designed,thus the stability and control of the system are realized.For time-vary descriptor Markovian jump systems,the problem of robust non-fragile H-infinity control is studied.First,the sufficient conditions are obtained through constructing Lyapunov-krasonskii functional and linear matrix inequalities to guarantee the closed-loop systems singular stochastic stability and satisfy the H-infinity performance index.Then,based on the theory of non-fragile control,a state feedback controller under controller gain perturbations with additive and multiplicative perturbations are considered respectively,so that the closed-loop system is stochastic stability and H-infinity control of the system is realized.