On a Nonstandard Model of Hybrid Automaton

Abstract

We discuss the description and analysis of Zeno phenomenon on the nonstandard hybrid automaton (NHA) which is a re-interpretation of a standard hybrid automaton in the domain of *R. We introduce the *cycle trajectory that is an infinite repetition of discrete state transition and prove that the convergence into *cycle is a necessary and sufficient condition for the existence of slightly extended Zeno. By using this condition, we show the existence of Zeno in the NHA of Fuller’s problem, and also give the simple way to escape from Zeno state (the regularization) for NHA.