Prolongation and stability of Zeno solutions to hybrid dynamical systems * *This work was supported by the German Federal Ministry of Education and Research (BMBF) as a part of the research project “LadeRamProdukt”.

Abstract

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.