On a symmetric discrete dynamics for hybrid systems

In this paper, we introduce a subclass of hybrid automaton called a symmetric hybrid automaton in which the continuous dynamics for each state is given by a transformation (diffeomorphism) from a core dynamics. Since the continuous dynamics is collapsed into the core dynamics in the symmetric hybrid automaton, we can deal with the properties of systems such as stability and reachability in the core dynamics. We focus on the discrete dynamics and the geometric properties, especially Zeno behavior, of a symmetric hybrid automaton.