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Global Stability and Asymptotic Gain Imply Input-to-State Stability for State-Dependent Switched Systems

In this paper we study several stability properties for state-dependent switched systems. We examine the gap between global asymptotic stability and uniform global asymptotic stability, and illustrate it with an example. Several regularity assumptions are proposed in order to obtain the equivalence between these two stability properties. Based on this equivalence, we are able to show that global stability and asymptotic gain imply input-to-state stability for state-dependent switched systems, which is the main result of the paper. The proof consists of a bypass via an auxiliary system which takes in a bounded disturbance, and showing that this system is uniformly globally asymptotically stable.