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

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.

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

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 gamma 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 gamma of filtering error systems is obtained. Finally, a numerical example is provided to demonstrate
the effectiveness of the proposed design method.