具有状态时滞的离散时间切换系统的H_∞滤波器设计：依赖状态的切换方法

H_∞ filtering for discrete-time switched systems with state delays:A state-dependent switching method

讨论一类时滞离散时间切换系统的H∞滤波器的设计问题.首先,当所有子系统都稳定时,基于切换Lyapunov函数和Finsler引理,得到了滤波误差系统渐近稳定且具有指定的H∞性能指标的充分条件,即使切换系统的每个子系统均不稳定,通过利用多Lyapunov函数方法和依赖状态的切换技术仍能保证切换系统稳定;然后,设计了H∞滤波器,并得到滤波误差系统满足指定的H∞性能指标的充分条件;最后,通过数值算例验证了所提出方法的有效性.

The problem of H∞ filtering for a class of discrete-time switched systems with delays is considered.When all the subsystems are stable,a sufficient condition for the asymptotic stability with the prescribed H∞ performance of filtering error systems is obtained based on switched Lyapunov function technique and Finsler lemma.Though each subsystem of the switched system is not stable,a stable switched system can be guaranteed by utilizing multiple Lyapunov functions method and state-dependent switching technique.Then,a desired H∞ filter can be designed and a sufficient condition with prescribed H∞ performance of filtering error systems is obtained.Finally,a numerical example is provided to demonstrate the effectiveness of the proposed design method.