A Passivity Analysis for Nonlinear Consensus on Balanced Digraphs

This work deals with the output consensus problems for multi-agent systems over balanced digraphs. While passivity-based approaches are widely used for analyzing undirected consensus protocols, we show that they are generally not applicable to the directed linear consensus protocol. To address this limitation, we propose a general approach that enables a passivity-based analysis for network systems with directed couplings. Then, we mitigate the complexity introduced by nonlinearities and directed interconnections by reformulating the general output consensus problem as a convergence analysis on a submanifold. Within this framework, we further focus on the stabilization problem, a specific form of the output consensus problem, and establish a sufficient passivity-based condition for stabilizing multi-agent systems over balanced digraphs. The results are supported by a numerical example.