通过基于驻留概率信息的方法, 研究了一类具有时变延迟离散切换系统的$H_{\mathrm{\infty }}$滤波器设计的问题. 通过对切换系统在每个子系统的驻留概率信息加以利用, 建立一种新型切换系统模型和滤波器模型. 利用Lyapunov函数及线性矩阵不等式方法, 给出切换系统的$H_{\mathrm{\infty }}$均方稳定的充分条件, 然后得到$H_{\mathrm{\infty }}$滤波器增益. 最后, 通过仿真算例来验证文章所用方法的有效性.

We propose a sojourn-probability-dependent method to investigate $H_{\mathrm{\infty }}$ filtering design for a class of discrete switched systems with time varying delay. A new type of switched system model and filter model is built by using the sojourn probability information. The sufficient condition of $H_{\mathrm{\infty }}$ mean square stability for switched systems is given via Lyapunov functional method. Then robust $H_{\mathrm{\infty }}$ filtering gains are derived. A numerical example is given to demonstrate the effectiveness and applicability of the proposed method.