A Characterization of Integral Input-to-state Stability for Hybrid Systems with Memory

TL;DR

This paper extends hybrid system theory to include memory effects by characterizing Integral Input-to-State Stability (iISS) using Lyapunov methods, dissipativity, and detectability, supported by a numerical example.

Contribution

It introduces a novel Lyapunov-based characterization of iISS for hybrid systems with memory, broadening the theoretical framework and control design tools.

Findings

Established equivalence among various stability descriptions.

Extended hybrid system theory to include time-delay effects.

Provided a numerical example illustrating the theoretical results.

Abstract

This paper addresses characterizations of Integral Input-to-State Stability (iISS) for hybrid systems with memory. Based on the Krasovskii approach, a novel Lyapunov characterization of iISS is established to extend the hybrid system theory to the time-delay case. In particular, we introduce the notions of dissipativity, detectability and storage functional to describe the iISS property from different perspectives. Under mild regularity and convexity assumptions, the equivalence relations among diverse stability descriptions are established, which lays a solid foundation for the control design. Finally, a numerical example is presented to illustrate the derived results.