Lyapunov-based sufficient conditions for stability of hybrid systems with memory

TL;DR

This paper develops Lyapunov-based criteria for the asymptotic stability of hybrid systems with memory, considering both hybrid and delay effects through generalized solutions on hybrid time domains.

Contribution

It introduces Lyapunov-Razumikhin and Lyapunov-Krasovskii methods for stability analysis of hybrid systems with memory, expanding existing techniques to more complex dynamical systems.

Findings

Established Lyapunov-based sufficient conditions for stability.

Provided examples illustrating the application of these conditions.

Extended stability analysis to hybrid systems with memory.

Abstract

Hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena. In this note, we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions. These generalized solutions, motivated by studying robustness and well-posedness of such systems, are defined on hybrid time domains and parameterized by both continuous and discrete time. We establish Lyapunov-based sufficient conditions for asymptotic stability using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals. Examples are provided to illustrate these conditions.