线性切换系统经周期切换渐近稳定性研究

研究一类含有两个子系统的线性切换系统经周期切换渐近稳定问题.首先给出了特殊周期切换,即等时切换下线性切换系统渐近稳定的充要条件;然后将所得结论进行了推广,使之适合于一般的周期切换情形,并结合自适应思想提出了实现系统周期切换的方法,使之能应用于工程实际.特别指出,一个系统可经切换达到二次稳定的充要条件是该系统可经周期切换渐近稳定.对于一类线性切换系统,采用周期切换可使切换信号的设计变得相对简单.仿真结果表明了所提出的方法简洁而有效.

Asymptotical stabilization of switched linear systems via periodic switching sequences

The asymptotical stabilization of switched linear systems with two subsystems via periodic switching sequences is discussed. A necessary and sufficient condition is derived for switched linear systems to be asymptotically stable. Moreover, a concrete method is proposed to design a periodic switching sequence. Especially it is pointed out that a system is quadratically stable under a switching sequence if and only if the system is asymptotically stable under a periodic switching sequence. The proposed theorems are convenient for judging whether a switched system is stable or not under a periodic switching sequence. Simulations show that the presented method is simple and effective.