Stabilization of Switched Linear Systems via LaSalle´s Invariance Principle

This paper considers the stability of switched linear systems. Assume a common weak quadratic Lyapunov function exists and the switches satisfy certain ergodic property, we investigate two extensions of LaSalle´s invariance principle. Unlike most existing results, the systems we investigated may have switching modes, which are not asymptotically stable. An application to the consensus of multi-agent systems is presented.