中文摘要：

切换系统是混杂动态系统的一种重要类型,具有广泛的应用背景,因此近年来得到许多学者的关注。对于切换系统稳定性的基本问题进行介绍,分别对任意切换下切换系统的渐近稳定性问题、某一切换策略下切换系统的渐近稳定性问题以及设计切换律镇定切换系统的问题进行了阐述,并对切换系统稳定性问题的研究方法,如单Lyapunov函数方法和多Lyapunov函数方法以及凸组合技术等做了相应的介绍。

英文摘要：

Switched system is an important class of hybrid dynamical systems. It is widely used in many aspects and has attracted a lot of attention. This paper mainly intrduces the basic problems for the stability of switched systems. Especially the stability of switched systems under any switching signal, the stability of switched systems under a given switching signal and designing a switching law to stabilizate the switched sytems are also discussed in this paper. And the methods to study the stability of switched systems are involved such as single-Lyapunov function, multi-Lyapunov function and technike of convex combinationg.