State feedback stabilization of invariant sets of switched systems

In order to discuss set stabilization of switched systems, a novel concept input-to-V (·) stability which extends the definition of input-to-state stability is proposed, where the function V (·) is a nonnegative function. Based on input-to-V (·) stability, conditions under which a class of switched systems can be effectively stabilized to an invariant set by state feedback are proposed. Rigorous proofs are given by using common Lyapunov function and multiple Lyapunov functions respectively. Simulation results are presented to verify our method.