A globally detectable hybrid system admits a smooth OSS-Lyapunov function

This paper presents Lyapunov and asymptotic characterizations of output-to-state stability (OSS) for hybrid systems, emphasizing that a globally detectable (i.e. nonuniform OSS) hybrid system admits a smooth exponential-decay OSS-Lyapunov function. Moreover, we construct the norm estimator for a globally detectable hybrid system.