%0 Journal Article
%T 一类离散时间无限状态马尔可夫跳跃系统H∞控制<br>H∞ Control for a Class of Discrete-Time Infinite State Markov Jump Systems
%A 何鑫
%A 严芳
%A 赵红霞
%A 贾亚琪
%A 张春梅
%J Dynamical Systems and Control
%P 139-148
%@ 2325-6761
%D 2023
%I Hans Publishing
%R 10.12677/DSC.2023.123015
%X 研究了一类具有同时受乘性噪声和无限马尔可夫跳参数影响的离散时间随机系统的控制问题。首先，给出了一个关于黎卡提方程解的线性不等式，通过求解线性不等式，构造了一个控制器，其次，利用算子理论和随机分析等知识给出离散时间随机系统的无限时域的有界实引理，并且通过一个耦合的黎卡提方程，证明了线性不等式的解和有界实引理之间的等价性。最后关于随机系统的一个线性反馈控制方案以黎卡提方程稳定解的线性矩阵不等式形式被提出，保证了随机控制系统的内部均方稳定性。<br />
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.
%K 无限状态马尔可夫跳跃系统，黎卡提方程，离散时间，H∞控制<br>Infinite State Markov Jump System
%K Riccati Equation
%K Discrete Time
%K H∞ Control
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=68368