Converse passivity theorems

Abstract

Passivity is an imperative concept and a widely utilized tool in the analysis and control of interconnected systems. It originates from the mathematical modelling of physical systems, including network synthesis and mechanical systems. It has also proved to be a key notion in adaptive and robust control. While many theorems on passivity are known in systems and control theory their converse statements have received much less attention. 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.