A characterization of integral input-to-state stability for hybrid systems

TL;DR

This paper provides a unified Lyapunov-based characterization of integral input-to-state stability (iISS) for hybrid systems, linking it to dissipativity, detectability, and robustness, with applications to sampled-data control systems.

Contribution

It introduces a comprehensive Lyapunov characterization of iISS for hybrid systems, extending existing theories and relating iISS to dissipativity and detectability notions.

Findings

Unified Lyapunov characterization of iISS for hybrid systems

Relation of iISS to dissipativity and detectability

Maximum sampling period ensuring iISS in sampled-data control

Abstract

This paper addresses characterizations of integral input-to-state stability (iISS) for hybrid systems. In particular, we give a Lyapunov characterization of iISS unifying and generalizing the existing theory for pure continuous-time and pure discrete-time systems. Moreover, iISS is related to dissipativity and detectability notions. Robustness of iISS to sufficiently small perturbations is also investigated. As an application of our results, we provide a maximum allowable sampling period guaranteeing iISS for sampled-data control systems with an emulated controller.