中文摘要：

将多Lyapunov函数方法推广至时滞情形，分析切换与时滞对于稳定性的影响，以Halanay不等式为引理，给出了与时滞相关的切换序列约束条件，以保证系统的指数稳定性，若时滞项消失，本文关于切换对于稳定性影响的分析与无时滞情形的相关结论是一致的，仿真结果说明了本文方法的有效性。

英文摘要：

The switched system consisting of a family of subsystems with delay is considered. In the time-delay situation, the multiple Lyapunov function approach is generalized to investigate the effect of switching and state-delay on stability. Using the Halanay inequality, the delay-dependent constraint condition on switching sequence is derived to guarantee the exponential stability. In the situation without time delay, the correspondent analysis result of switching effect on stability is a special case of our conclusions. Numerical examples are given to demonstrate the proposed approach.