Research On Control And H_? Filtering Of Discrete Stochastic Systems

Discrete-time stochastic systems have attracted much attention because of its wide application in computer technology,wireless communication network,system biology and other fields.The control and filtering of discrete-time stochastic systems have become a hot research direction of control theory.This thesis introduces three kinds of second-moment state transition matrices for linear discrete-time stochastic systems,and through the obtained state transition matrices,the necessary and sufficient conditions for finite-time stability,mean square stability,and mean square asymptotic stability are given.We establish the connection between the state transition matrix and a new Lyapunov func-tion.Subsequently,the state transition matrix method is successfully extended to the fault-tolerant control of linear discrete time-varying stochastic systems and the finite-time non-fragile control of linear discrete mean-field systems.For general nonlinear discrete systems,a new bounded real lemma independent of the mathematical expectation of state trajectories is given.We obtain existence conditions of H_?filtering and H₂/H_?filtering.Based on this method,a set of event-triggered H_?filtering schemes are designed.The main research results and innovations of this thesis are summarized as follows:1.For the first time,the second-moment state transition matrix method is used to solve the stability and stabilization problems of linear discrete time-varying stochastic systems.The necessary and sufficient conditions for finite-time stability,circle stability,mean square stability,and mean square asymptotic stability are given.Based on the state transition matrix,a new Lyapunov-type condition is constructed,which not only has the advantage of non-conservativeness of the state transition matrix,but also can easily design a stabilizing controller.2.The problem of fault estimation and fault-tolerant control for linear discrete time-varying stochastic systems is studied.A scheme that can realize state and fault estimation and fault-tolerant control is proposed.For all kinds of fault signals,the convergence of fault estimation error can be guaranteed.With the help of the state transition matrix method and cone compensation linearization technique,two different controller parame-ter design methods are given.Under the effect of fault compensation,the stabilization of the closed-loop system is realized.3.The method of the state transition matrix for discrete mean-field time-varying stochastic systems is proposed for the first time.Based on this method,several necessary and sufficient conditions for finite-time stabilization of mean-field stochastic systems are obtained.The finite-time stabilization criterion derived from the state transition matrix often leads to computational complexity over time.Therefore,the criterion is successfully transformed into linear matrix inequalities,which make the design of finite-time stabiliz-ing controller easier.4.The H_?filtering of general nonlinear discrete time-varying stochastic systems is studied.We give a stochastic bounded real lemma based on a new Hamilton-Jacobi inequality,where the Hamilton-Jacobi inequality does not depend on the mathemati-cal expectation of states or external disturbances.To optimize the estimation error,an H₂/H_?filter is designed.Moreover,the theory is successfully extended to the event-triggered nonlinear discrete time-varying filtering problem.Finally,the conclusions and some topics for future work are given.