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.