A multiple Lyapunov functions approach for stability of switched systems

In this paper, a multiple Lyapunov functions based approach is presented for the stability analysis for switched systems. Compared with existing Multiple Lyapunov functions approaches in the literature, this approach requires less conservative conditions on the constituent subsystems. The stability theorem proposed here gives not only Lyapunov stability, but asymptotic stability as well. In particular, the result presented here allows the switched system to have different states, and for some of the subsystems to be unstable or to lack a common equilibrium point.