On Control-Lyapunov Functions for Hybrid Time-Varying Systems

We explicitly construct strict input-to-state stable Lyapunov functions for time varying hybrid systems, in terms of given nonstrict Lyapunov functions and persistency of excitation parameters. This provides a hybrid analog of our earlier continuous time Lyapunov function constructions. Our results are new even for the special case of discrete time systems since our formulas involve finite sums of persistency of excitation parameters. We also construct explicit strict Lyapunov functions for systems satisfying appropriate nonstrict hybrid analogs of the conditions from Matrosov´s theorem