Analysis And Control For Stochastic Markov Jump Systems

Many practical systems experience abrupt changes in their structure and parameters，caused by phenomena as component failures or repairs, changing subsysteminterconnections，and abrupt environmental disturbances. Then the systems are driven byMarkov systems. This class of system contains two components. The first component is mode,which is described by a finite state Markov process. The second component is state, which ineach mode is denoted by a stochastic differential equation. Markov jump systems haveattracted much attention because of practical deep background. Analysis and control forstochastic Markov jump system are very important in control and its applicants.The paper mainly studied stochastic stability, robust H_∞control, robust guaranteed costcontrol and design filtering of stochastic Markov jump system. The contributions can beconcluded as follows:1. The problem of Memory-less robust H_∞control for stochastic Markov jump system isstudied. According to a class of uncertain stochastic time-delay Markov jump system withstate and input delays, a memory-less state feedback controller on Lyapunov-Krasovskiifunction and stochastic differential equations is designed to make the closed-loop systemrobust stochastic stable and meet H_∞performance for all admitted uncertainties. Finally, asufficient condition for the solvability of this problem is given in the form of linear matrixinequalities.2. The problem of Memory robust H_∞control for stochastic Markov jump system isstudied. According to a class of uncertain stochastic time-delay Markov jump system withstate and input delays, a memory state feedback controller on Lyapunov-Krasovskii functionand stochastic differential equations is designed to make the closed-loop system robuststochastic stable and meet H_∞performance for all admitted uncertainties. Finally, a sufficientcondition for the solvability of this problem is given in the form of linear matrix inequalities,bacause of time-delay in the controller, the method is wider and the conservation is smallerthan before, and it is much easier to implement and apply in practice.3. The problem of robust guaranteed cost control for stochastic Markov jump system isstudied. A controller is designed to make the closed-loop system robust stochastic stable and meet H_∞performance, and exist a minimum upper bound. Finally, using linear matrixinequalities methods, the design of robust guaranteed cost controller is given.Theconservation of result is smaller and is more convenient to apply, and the numericalsimulation and image simulation prove the validity of this method.4. The problem of robust filtering for stochastic Markov jump system is studied.According to a class of uncertain stochastic time-delay Markov jump system with state andinput delays, the purpose of this problem is design a full filter such as the dynamics of theestimation error is guaranteed to be stochastically stable and meet H_∞performance for alladmitted uncertainties. Finally, filter controller is designed in terms of linear matrixinequalities. By using toolbox in Matlab, it is easily to obtain controller gain matrices. Theconservation of result is smaller and is more convenient to apply, and the numericalsimulation proves the feasibility of this method.