Converse passivity theorems

TL;DR

This paper develops converse passivity theorems for nonlinear feedback systems, showing that open-loop passivity is necessary for closed-loop passivity and that feedback stability implies system passivity.

Contribution

It introduces new converse passivity theorems for nonlinear systems, linking open-loop passivity and feedback stability to system passivity.

Findings

Open-loop passivity is necessary for closed-loop passivity.

Feedback stability of a system with passive systems implies the system's passivity.

Various versions of converse passivity theorems are established for nonlinear feedback systems.

Abstract

Passivity is an imperative concept and a widely utilized tool in the analysis and control of interconnected systems. It naturally arises in the modelling of physical systems involving passive elements and dynamics. While many theorems on passivity are known in the theory of robust control, very few converse passivity results exist. This paper establishes various versions of converse passivity theorems for nonlinear feedback systems. In particular, open-loop passivity is shown to be necessary to ensure closed-loop passivity from an input-output perspective. Moreover, the stability of the feedback interconnection of a specific system with an arbitrary passive system is shown to imply passivity of the system itself.