Existence And Stabilization Problem For Nonlinear Systems Lyapunov Function

In this paper we present a converse Lyapunov theorem for globally uniform asymptotically controllably switched systems.And we consider general nonlinear switched systems.Under an additional assumption,we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense.Finally,the controllability of a sort of special Linear Image processing model and its switched model are discussed.A necessary condition and a sufficient condition have been presented for the former and a necessary condition for the latter.