Nodal Consensus in Multiagent Systems With Edge Communications

In this article, we studies the nodal consensus in multiagent systems subject to edge communications. It is revealed that the edge communication can be modeled as perturbations to the nodal network, and the multiagent network is then equivalent to a feedback loop introducing a negative feedback element to the edge dynamics. In virtue of this, a two-layer network perspective is adopted in studying the nodal consensus, where it is shown that the behavior of edge communication is essentially an image of a finite-gain \mathcal {L}_{2}-stable operator acting on the node-layer network, whose operator norm is limited by the nodal dynamics, the edge dynamics and the communication topologies of both the node-layer and the edge-layer. Then, the robust nodal consensus subject to edge communications against additive nodal uncertainties is discussed. The quantitative relationship of the nodal dynamics, the edge dynamics, the structure of the two-layer communication network and the robustness against the nodal uncertainties and the edge-communication uncertainties are characterized. We also extend our results to the edge-preserving consensus, which is based on characterizing the structured uncertainties to the nodal networks. Simulation examples are finally provided to show the effectiveness of the theoretical results.