一类切换系统的稳定性分析与镇定控制

利用基于切换二次Lyapunov函数的存在性证明切换系统的渐近稳定性,研究了一类离散时间切换系统的稳定性分析与镇定控制问题.对一些子系统的状态分区采用外部的椭圆体或者退化的椭圆体加以近似,因而能够利用S-Procedure降低方法的保守性.指出切换系统稳定性的证明及状态反馈控制器的设计都可看作线性矩阵不等式(LMI)的可行性问题而进行有效的求解.

Stability analysis and stabilization control for a class of switched systems

The problem of stability analysis and stabilization control of a class of discrete-time switched system is addressed, and the method used is to prove asymptotic stability of the switched systems based on the existence of switched quadratic Lyapunov functions. The state regions of some subsystems are approximated by outer ellipsoids or degenerate ellipsoids, and thus the method is enabled to reduce conservatism by using S-procedure. It is shown that proving stability and designing state-feedback controllers of the switched system can be cast as feasibility problems involving linear matrix inequalities, which can be solved efficiently.