Prolongation and stability of Zeno solutions to hybrid dynamical systems

Abstract

The paper proposes a framework for the construction of solutions to a hybrid dynamical system that exhibit Zeno behavior. A new approach that enables solution to be prolonged after reaching its Zeno time is developed. It allows for a comprehensive stability analysis and asymptotic behavior characterization of such solutions. The results are applicable to a wide class of hybrid systems and match with practical experience of simulation of real-world phenomena. Moreover they are potentially useful for applications to interconnections of hybrid systems.