网络化马尔可夫跳变系统的鲁棒无源控制

Robust Passive Control of Networked Markovian Jump Systems

针对基于网络的凸多面体不确定离散时间马尔可夫跳变系统,研究其鲁棒无源控制问题.在网络诱导时滞是时变且有界的情况下,基于李雅普诺夫稳定性理论,通过构造参数依赖的随机李雅普诺夫泛函和运用广义系统变换,提出了不依赖模态的无源控制器存在的时滞依赖充分条件.所设计的鲁棒无源控制器保证了相应的闭环系统是鲁棒随机稳定且具有指定耗散率.将鲁棒无源控制器设计问题转化为一组线性矩阵不等式的可解性问题.仿真算例证明了本文方法的有效性.

This paper is concerned with the problem of robust passive control for networkbased discrete-time Markovian jump linear systems with polytopic uncertainty. The network- induced delay is considered to be time-varying and bounded. Based on Lyapunov stability theory, a delay-dependent sufficient condition for the existence of a mode-independent passive controller is proposed by constructing parameter-dependent stochastic Lyapunov functional and by using descriptor system transformation. The proposed controller ensures both robust stochastic stability and a prescribed dissipation rate for the resulting closed-loop system. The problem can be solved in terms of a set of linear matrix inequalities. A simulation example is provided to demonstrate the effectiveness of the proposed method.