Interconnection of Discrete-Time Dissipative Systems

Andrea Martinelli, Ahmed Aboudonia, John Lygeros

Published 2023-11-14Version 1

Strictly proper discrete-time (DT) systems cannot be passive. In order for passivity-based control to be exploited nevertheless, some authors introduce virtual outputs, while some others rely on continuous-time passivity and then apply discretization techniques that preserve passivity in DT. In this manuscript, we argue that quadratic supply rates incorporate and extend the effect of virtual outputs, allowing one to exploit dissipativity properties directly in DT. We derive local dissipativity conditions for a set of nonlinear systems interconnected with arbitrary topology, so that the overall network is guaranteed to be stable. In case of linear systems, we develop feedback dissipativity conditions that are linear in the supply rate. To demonstrate the validity of our methods, we provide numerical examples in the context of islanded microgrids.