Dynamical properties of hybrid automata

Hybrid automata provide a language for modeling and analyzing digital and analogue computations in real-time systems.Hybrid automata are studied here from a dynamical systems perspective.Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized.The results on existence, uniqueness, and continuity serve as a starting point for stability analysis.Lyapunov's theorem on stability via linearization and LaSalle's invariance principle are generalized to hybrid automata.