Semistability and Robustness Analysis for Switched Systems

This article develops some new results on semistability of switched systems using multiple Lyapunov functions. The main results of the article involve sufficient conditions for guaranteeing semistability of switched systems using multiple Lyapunov functions and a class of switching conditions. Moreover, converse Lyapunov theorems for a finite family of pairwise commuting semistable systems are also developed. Using these stability results and an extended notion of homogeneity for switched systems, we derive some robustness results for semistability of switched systems.