离散马尔科夫跳变系统模态不依赖非脆弱H_∞控制

Mode-independent Non-fragile H_∞ Control for Discrete-time Markovian Jump System

针对跳变系统跳变参数无法获取的情形,考虑待设计控制器增益存在乘性范数有界不确定摄动,研究了离散马尔科夫跳变系统的模态不依赖非脆弱H∞控制问题.基于几个重要引理,导出了模态不依赖非脆弱状态反馈H∞控制器存在的以耦合线性矩阵不等式形式表达的充分条件,并给出了确定控制器参数的显示表达式.最后给出一个具体算例,利用Matlab7.0的LMI工具箱进行数值仿真,通过求取相应的状态响应和输出响应曲线,并与在设计阶段不考虑控制器参数摄动的常规H∞状态反馈控制器设计方法的结果进行比较,演示了所提出方法的有效性和优越性.

For the case that the jump parameters of discrete-time Markovian jump system is not available, this paper deals with the problem of mode-independent non-fragile H∞, control for discrete-time Markovian jump system considering the presence of multiplicative bounded controller parameter variations. The sufficient conditon on the existence of mode-independent non-fragile state feedback H∞ controller is derived based on several important lemmas in terms of a set of coupled linear matrix inequalities （LMIs）, and an explicit expression of a required controller is also given. By employing the LMI toolbox of Matlab 7.0 for numercial simulation, an example is finally provided to demonstrate the effectiveness and superiority of the proposed approach through the state response curves and the output response curve and also by comparison with normal method of H∞, controller design in which controller parameter variation are not considered beforhand.