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H∞ Control for a Class of Discrete-Time Infinite State Markov Jump Systems

DOI: 10.12677/DSC.2023.123015, PP. 139-148

Keywords: 无限状态马尔可夫跳跃系统,黎卡提方程,离散时间,H∞控制
Infinite State Markov Jump System
, Riccati Equation, Discrete Time, H∞ Control

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The control problem of a class of discrete-time stochastic systems affected by multiplicative noise and infinite Markov jump parameters is studied. Firstly, a linear inequality about the solution of Riccati equation is given, and a controller is constructed by solving the linear inequality. Secondly, the bounded real lemma in infinite time domain of discrete-time stochastic systems is given by using the knowledge of operator theory and stochastic analysis. Through a coupled Riccati equation, the equivalence between the solution of linear inequality and bounded real lemma is proved. Finally, a linear feedback control scheme for stochastic systems is proposed in the form of linear matrix inequality of the stable solution of Riccati equation, which ensures the internal mean square stability of stochastic control systems.


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