切换系统由一组子系统和切换规则组成,其中切换规则对系统的稳定性及动态性能起着至关重要的作用.不同于现有的切换规则,文章针对一类子系统为离散时滞系统的切换系统,利用系统停留在每个子系统的概率信息, 引入驻留概率信息,研究系统的鲁棒$H_{\mathrm{\infty }}$ 控制问题.基于多Lyapunov泛函和线性矩阵不等式方法,给出切换系统的鲁棒$H_{\mathrm{\infty }}$均方稳定的充分条件.需要指出的是,最终系统的稳定条件依赖于系统的驻留概率信息.最后,通过仿真算例证明所用方法的有效性.

Switched systems are composed of a set of subsystems and switch rules, wherein the switching rules are important and can affect the stability and dynamic performance of the system. Different from the existing switch rules, this paper uses the information of the probability information of the switched system on each subsystems, which is called sojourn probability information. By using these information, new kinds of switched system model is built and the problem of robust $H_{\mathrm{\infty }}$ control is considered for a class of discrete switch systems with input delays. Then sufficient conditions of the robust $H_{\mathrm{\infty }}$ mean square stability of the system are derived via multiple Lyapunov functional method and LMI technique. It should be pointed out that the final stable condition depends on the values of sojourn probabilities. At last, one numerical example is proposed to show the effectiveness of the proposed model and method.