Abstract: Robust H∞ filter for a class of parameter uncertain switched systems using Delta operator has been discussed. Based on multiple Lyapunov function theory and average dwell time, a sufficient condition for the existence of stability of the parameter uncertain Delta operator switched system is presented in terms of LMI, and the H∞ filter performance is analyzed. Furthermore, the sufficient existence conditions and designing method of robust H∞ filter are proposed. The designed robust H∞ filter not only guarantees the closed-loop system with uncertain parameter to be asymptotically stable, but also satisfies H∞ performance that expected. A simulation example is given to illustrate the effectiveness and feasibility of the proposed method.

Key words: H&infin, filter, switched system, average dwell time, Delta operator

摘要： 研究了一类参数不确定线性Delta算子切换系统的鲁棒H∞滤波器设计问题。提出利用多Lyapunov函数和平均驻留时间方法，以线性矩阵不等式的形式给出了参数不确定Delta算子滤波误差切换系统指数稳定性条件，并进行了H∞性能分析，从而进一步给出Delta算子切换系统鲁棒H∞滤波器存在的充分条件和设计方法。所设计的滤波器不但保证系统参数不确定时闭环系统指数稳定，而且满足所期望的H∞性能指标。仿真结果证明了设计方法的有效性和可行性。

关键词: H&infin, 滤波器, 切换系统, 平均驻留时间, Delta算子