Title: Converse passivity theorems,
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.