Stability Analysis And Control Of Markov Jump Time Delay Systems

As a special kind of hybrid system,Markov jump system is more and more widely used in social life,such as the application in aircraft control system,in the medical system to predict the development trend of disease,as well as in the economic system for the prediction of market share and sales expected profit forecast,so the research on the stability and control of Markov jump system appears especially important.In addition,the time-varying delay phenomenon is common in Markov jump system,which usually causes system instability and affects the performance of the system.Therefore,it is realistic to explore the control problem of Markov jump system with time-varying time delay.Meaning and theoretical value.The study of the control problem of Markov jump system with time-varying time delay is more relistic and theoretical.This paper uses Lyapunov functional and linear matrix inequalities to studying the slid-ing mode control of generalized Markov jump systems and the random sampled-data control of Markov jump systems.The main work is as follows:Firstly,the stochastic admissibility of generalized Markov jump systems with time-varying delays is studied.By constructing an integral sliding mode switching function,combining the Wirtinger inequality and the formula based on the extension of the Wirtinger inequality,some sufficient conditions for random admissibility are derived.Then the slid-ing mode controller and switching rules are designed so that the state trajectory reaches the sliding mode surface in a limited time,thereby obtaining stable sliding mode dynamics.Secondly,this paper considered the sliding mode control problem of generalized Markov jump system with time-varying delay and disturbance.By establish an integral sliding mode surface and design an equivalent controller,then construct a Lyapunov functional with triple integral terms,use Jensen's inequality and more accurate scaling methods,the corresponding controller gain matrix and H? Performance are obtained.Finally,the random sampling control problem of Markov system with time-varying delay and disturbance is discussed.Design a random sampling controller,construct a Lya-punov functional related to the sampling information,use the extended formula based on the Wirtinger inequality,some sufficient conditions are obtained for the asymptotic stability of the system.And then the convex combination technique is useed to solve the system's H?performance index.