Finite Time Sliding Mode Control Of Markov Jump System

Markov Jump Systems(MJSs)is a kind of complex stochastic system that has attracted much attention.It can effectively describe the mutation of system mode,and provides a wide range of space and important theoretical basis for the description of system model.On the other hand,the concept of Finite Time Stability(FTS)is applied to analyze the convergence of system state in short time intervals,which is an effective method to study the actual system transient performance.Unfortunately,most of the current research on sliding mode control focuses on the infinite operating time range.Therefore,it is necessary to study the problem of sliding mode control for finite time dynamic systems.As a high-performance robust control strategy,Sliding Mode Control(SMC)has the advantages of being insensitive to parameter perturbation,good transient performance,fast response speed and strong robustness.In this paper,the robust control of Markov jump system is studied by combining sliding mode control theory and finite time theory.The detailed arrangement of this paper is as follows:The first chapter mainly introduces the research background and significance of the subject,as well as the development status of Markov jump system,sliding mode control system and finite time stability.Chapter 2 gives the definition and lemma required in this paper,and introduces relevant concepts.In chapter 3,the finite time sliding mode controller of Markov jump system with time delay is studied.For a class of nonlinear markov jump systems with time-varying delays and external disturbances,the problem of finite time sliding mode control is studied.An integral sliding mode function is constructed and a corresponding sliding mode control law is designed to drive the state trajectory to the specified sliding mode surface within a finite time interval.By using the relaxation matrix method,sufficient conditions for the closed loop system to be bounded in a finite time interval are obtained.An example verifies the validity of the conclusion.In chapter 4,the finite time sliding mode controller design of stochastic Markov jump system is studied.By means of sliding mode control,the finite time sliding mode control problem of uncertain random Markov jump system is discussed.The key problem to be considered is how to guarantee the random finite time stability and the accessibility of the sliding surface of the closed-loop system within a given finite time interval.For this purpose,a parameter-dependent sliding mode control law will be designed to make the state trajectory move along the specified sliding mode surface in a finite time interval and determine the upper bound of the sliding domain.Next,sufficient conditions to ensure the stability of the slidingmode control system in the arrival stage and the sliding stage are established by using the partition strategy.Finally,numerical examples show the correctness of the conclusions in this chapter.Chapter five summarizes the research problems and the future development direction of this paper.