On ϱ-passivity

We discuss passivity beyond continuous-time systems by highlighting several inconsistencies of the definition currently in use, for instance when applied to discrete-time systems, and by motivating the need for a new and more consistent notion. Hence, we propose a new definition, ϱ-passivity, that addresses the raised issues and that, as a result, is naturally applicable to a larger class of systems including discrete-time systems with non-zero relative degree. We show that, in line with the classical definition, ϱ-passivity is preserved under parallel and negative-feedback interconnection. These are preliminary results aimed at bridging passivity between different time domains, and taking the first step towards a more comprehensive and consistent passivity theory.