On the existence of Zeno behavior in hybrid systems with non-isolated Zeno equilibria

Abstract

This paper presents proof-certificate based sufficient conditions for the existence of Zeno behavior in hybrid systems near non-isolated Zeno equilibria. To establish these conditions, we first prove sufficient conditions for Zeno behavior in a special class of hybrid systems termed first quadrant interval hybrid systems. The proof-certificate sufficient conditions are then obtained through a collection of functions that effectively ¿reduce¿ a general hybrid system to a first quadrant interval hybrid system. This paper concludes with an application of these ideas to Lagrangian hybrid systems, resulting in easily verifiable sufficient conditions for Zeno behavior.