Dynamic Analysis And Control Of Discrete-time Stochastic Systems With Infinite State Space Markov Switching

Due to the influence of the environment and other factors on the actual system,the state space of the Markov chain valued on a countable set.In order to describe the models of stochastic systems more accurately,it is a great significance to study Markov-switched stochastic systems with infinite state spaces.We mainly discusses the stability of discrete stochastic systems with infinite Markov switching,controller design,and infinite hoaizon hybridH₂/H_?control.The main research contents are summarized as follows:1.The stability of a class of discrete-time time-varying stochastic systems with infinite Markov switching is studied.Firstly,the relationship between the anti-causal evolution operator and the conditional expectation is given by using the linear positive bound operator,stochastic analysis and other methods.Secondly,some main results are given,that is,the strong exponentially stable in mean square and the exponentially stable in mean square with conditions are equivalent to each other under the certain conditions of the transition probability matrix is non-degenerate of Markov Chains,and the positive bounded solution of the Lyapunov equation is obtained.In addition,the relationship between the internal stability and thel² input-output stability of the system is given in the case of finite energy external random perturbation.Finally,an example is given to verify its correctness and validity.2.The stability and control of a class of discrete-time stochastic systems with simultaneous multiplicative noise and infinite Markov jump parameters are studied.Firstly,a linear feedback control scheme of stochastic systems is proposed in the form of linear matrix inequalities for stable solutions of the Riccati equation,which guarantees the internal mean square stability of stochastic systems;Secondly,under the assumption of uniform observability,using the stochastic analysis,we explore the relationship between the exponentially stability in mean square of infinite Markov switching discrete-time stochastic system and the positive bounded solution of the Riccati equation;Thirdly,four coupled matrix Riccati equations(CMREs)are constructed according to the feedback control scheme combined with Riccati equation,and the necessary and sufficient conditions for the existence of the hybrid infinite horizonH₂/H_?control problem with four coupled matrix Riccati equations(CMREs)are given.Finally,the state feedback H₂/H_?controller is constructed by solving CMREs.