Input-to-State Stability, integral Input-to-State Stability, and $\mathcal{L}_2$-Gain Properties: Qualitative Equivalences and Interconnected Systems

TL;DR

This paper explores the relationship between input-to-state stability (ISS) and $\\mathcal{L}_2$-gain properties, establishing qualitative equivalences and deriving new stability conditions for interconnected nonlinear systems.

Contribution

It demonstrates qualitative equivalences between ISS and $\mathcal{L}_2$-gain properties and introduces new sufficient conditions for the stability of interconnected systems based on these equivalences.

Findings

Qualitative equivalences between ISS and $\mathcal{L}_2$-gain properties established.

New sufficient conditions for stability of interconnected systems derived.

Enhanced understanding of robustness properties in nonlinear system analysis.

Abstract

Input-to-state stability (ISS) and $\mathcal{L}_2$-gain are well-known robust stability properties that continue to find wide application in the analysis and control of nonlinear dynamical systems and their interconnections. We investigate the relationship between ISS-type and $\mathcal{L}_2$-gain properties, demonstrating several qualitative equivalences between these two approaches. We subsequently present several new sufficient conditions for the stability of interconnected systems derived by exploiting these qualitative equivalences.