Research On State Feedback Controller Design Of Stochastic Time-delay Markovian Jump Systems

In practice,Markovian Jump Systems have served as convenient tools for analyzing plants subjected to random abrupt changes,which may result from random failures,repair of components,changing subsystem interconnections,sudden environmental disturbances and etc.Due to their extensive applications in Robot Operating System,Ship Motion Control,Aircraft Control,Economic System and other areas,more and more attention has been paid to the problem of stability and stabilization for Markovian Jump Systems.The purpose of this dissertation is to investigate the problem of controller design of Stochastic Time-delay Markovian Jump Systems(STMJSs).The main results of this dissertation are as follows:(1)First,considering non-fragile control of STMJSs with partly unknown transition rates,by means of Lyapunov methodology,a mode-dependent non-fragile state feedback controller is designed to guarantee stochastic stability of the corresponding closed-loop system.A linear matrix inequality approach is employed to obtain the controller parame-ters.(2)And then,the problem of H? control for STMJSs with partly unknown transition rates and input saturation is investigated.By employing more appropriate Lyapunov-Krasovskii functional,a state feedback controller is designed to guarantee the stochastic stability of the corresponding closed-loop system with H? performance.(3)Thridly,the approach of design robust non-fragile state feedback controller for STMJSs with partly unknown transition rates is investigated in this paper.By using appro-priate type Lyapunov-Krasovskii functional and convex combination method,sufficient conditions for robust stochastic stability of Markovian jump systems with less conserva-tive are proposed.Then,a non-fragile state feedback controller is constructed such that the closed-loop Markovian jump systems are stochastically stable.(4)Moreover,a non-fragile controller is designed for STMJSs with generally uncer-tain transition rates.To begin with,for STMJSs,based on the properties of the relation-ship between the transition rates and the mode-dependent Lyapunov-Krasovskii function-al,controller gain matrices are obtained so that the closed-loop system is stochastically stable.All the proposed conditions are given in the term of linear matrix inequalities.(5)Besides,finite-time dissipativity analysis and controller design for STMJSs with generally uncertain transition rates are concerned.By constructing the more appropri-ate Lyapunov-Krasovskii functional,sufficient conditions for finite-time dissipativity of the STMJSs are proposed which are rarely mentioned before.Then,a state feedback controller is designed such that the closed-loop Markovian jump system is finite-time dissipative.Finally,the results of the dissertation are summarized and further research topics are pointed out.