带时滞二阶时变线性脉冲切换系统的稳定性分析

本文利用Lyapunov 函数研究了一类带时滞的二阶时变线性脉冲切换系统的指数稳定性。我们得出这样的结论: 为了保证切换系统在确定切换律下指数稳定, 只需对每一子系统在相应切换区间子序列上加以适当控制, 这些控制的要求远弱于使每一子系统稳定的要求。除此之外, 我们也给出了切换系统在任意切换律下的指数稳定性结果, 并利用相关的结论给出切换律的设计方法。

Stability Analysis of a Class of Second Order Impulsive Switched Systems

By using lyapunov functions,we investigate a class of switched systems with delays which are effected by fixed time impulses.Some sufficient conditions for exponential stability of the systems are established.In our results,we show that,for the stability of switched systems under a given switching law,we should only give every subsystem some suitable controls in a series of corresponding subintervals of switching intervals,and the demands of these controls are much weaker than those making every subsystem stable.In addition,we also discuss the esponential stability of the systems under arbitrary switching laws and the design of switching law.