Passivity Compensation: A Distributed Approach for Consensus Analysis in Heterogeneous Networks

Abstract: This paper investigates a passivity-based approach to output consensus analysis in heterogeneous networks composed of non-identical agents coupled via nonlinear interactions, in the presence of measurement and/or communication noise. Focusing on agents that are input-feedforward passive (IFP), we first examine whether a shortage of passivity in some agents can be compensated by a passivity surplus in others, in the sense of preserving the passivity of the transformed open-loop system defined by the agent dynamics and network topology. We show that such compensation is only feasible when at most one agent lacks passivity, and we characterise how this deficit can be offset using the excess passivity within the group of agents. For general networks, we then investigate passivity compensation within the feedback interconnection by leveraging the passivity surplus in the coupling links to locally compensate for the lack of passivity in the adjacent agents. In particular, a distributed condition, expressed in terms of passivity indices and coupling gains, is derived to ensure output consensus of the interconnected network.