离散时间切换广义系统的一致有限时间稳定性

摘要

针对一类离散时间切换广义系统，研究其一致有限时间稳定性问题．首先，把广义系统的有限时间稳定性概念推广到离散切换广义系统；然后，利用Lyapunov—like函数方法，给出了离散切换广义系统在任意给定的切换规则下是正则、因果的，且有限时间有界和有限时间稳定的充分条件，同时给出了保证离散切换广义系统一致有限时间稳定的状态反馈控制器的具体设计方法．仿真算例结果说明了该控制方法的有效性．%The problem of uniform finite-time stability for a class of discrete-time switched descriptor systems is considered. Firstly, the concept of finite-time stability for continuous descriptor systems is extended to discrete-time switched descriptor systems. Secondly, based on the Lyapunov-like function method, and under arbitrary switching signal, sufficient conditions under which discrete-time switched descriptor systems are regular and causal, uniform finite-time bounded and uniform finite-time stable, are derived. Furthermore, the state feedback controllers are designed to guarantee the discrete-time switched descriptor system uniform finite-time stable. Finally, some numerical examples show that the results obtained in this paper are effective.