具有时变时滞的离散切换系统基于观测器的H_∞控制

Based-observer H_∞ control for discrete-time switched systems with time-varying delays in state

利用多Lyapunov函数方法,研究一类具有时变时滞的线性离散切换系统基于观测器的H∞控制问题.通过设计对角分块形式的多Lyapunov函数矩阵,使切换律只依赖于观测状态.在基于观测器的切换反馈控制策略下,给出了系统实现H∞控制的充分条件,且条件可以表示为与时滞界相关的线性矩阵不等式(LMI)的形式,同时还给出了切换律、观测器和控制器的设计方案.最后用一个仿真例子表明了结论的有效性.

The problems of observer-based H∞ control and the design of switching law are addressed for a class of linear discrete-time switched systems with time-varying delay in state by using multiple Lyapunov function technique. A novel multiple Lyapunov function matrix with diagonal-block form is devised to solve the difficulties in designing switching law. Under observer-based switching feedback, a delay-dependent LMI-based sufficient condition for the problem is derived. The corresponding H∞ controllers, observers and observer-state-dependent switched law are simultaneously designed. Finally, a simulation example shows the effectiveness of the results.