Prolongation and stability of Zeno solutions to hybrid dynamical systems

TL;DR

This paper introduces a new framework for extending solutions past Zeno points in hybrid dynamical systems, enabling stability analysis and broad applicability to real-world phenomena and interconnected systems.

Contribution

A novel approach for prolonging Zeno solutions in hybrid systems, facilitating stability analysis and practical simulation of complex hybrid behaviors.

Findings

Framework successfully prolongs Zeno solutions

Enables comprehensive stability analysis

Applicable to various real-world hybrid 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.