Design Of Several Kinds Of Controller For Markov Jump System

With the continuous in-depth study of the control theory by experts and scholars,it is found that the structure and parameters of the system in the actual industrial production process will be changed due to the change of external environment and its own faults and other factors.Such system is called the hybrid system.For hybrid systems,Markov jump systems are often modeled by scholars to study the stability of the system and the design of the controller under several kinds of conditions.In actual industrial production,controller failure is a very common and challenging control problem,which has been the focus of research by many experts and scholars.Therefore,it is of practical significance to propose a control system with better stability and less conservatism.In this paper,a system model of which the change signal of the system matrix conforms to the Markov stochastic process is established,and several kinds of controller design problems are studied by means of linear matrix inequality and Lyapurov function.This paper mainly studies the failure problem of the controller,the design of periodic switching controller and the design of guaranteed cost controller.The specific research work is as follows:（1）It studies the controller design problem of system switching signal conforming to Markov stochastic process and controller switching signal being general random switching signal.A class of controllers with periodic random switching signals is designed and the design of controllers with aperiodic random switching signals is extended.The stabilization problem of continuous-time Markov jump system with the above-mentioned controller is studied.In the form of linear matrix inequality,sufficient conditions to be satisfied are given.（2）The design of guaranteed cost control for continuous-time Markov jump system is studied.The continuous-time Markov jump system is discretized,and the sufficient condition for the stability of the system is given in the form of linear matrix inequality（LMI）.Finally,a practical example is given to verify the effectiveness of the proposed method.（3）The exponential almost sure stability（EAS）and stabilization of continuous-time Markov jump systems under continuous controller failure are studied.A piecewise constant function is introduced to describe the system switching between open-loop and closed-loop.Then,the sufficient conditions for the stability of the EAS were established by using the stochastic state transfer matrix and Lyapurov method.In addition,the statistical transient properties of Markov stochastic processes are considered,and the control gain is obtained by solving Lyapunov equation.