MAS Consensus and Delay Limits Under Delayed Output Feedback

In this technical note, we study the consensus problem for discrete-time multi-agent systems over an undirected, fixed network communication graph, focusing on the robustness of consensus with respect to communication delay. We assume that the agents' input is subject to a constant albeit possibly unknown time delay, and is generated by a distributed dynamic output feedback control protocol. Drawing upon concepts and techniques from robust control, notably those concerning gain margin optimization and analytic interpolation, we derive explicit, closed-form conditions for general linear agents to achieve consensus. Our results display an explicit dependence of the consensus condition on the delay value as well as on the agent's unstable poles and non-minimum phase zeros, showing that delayed communication between agents will generally hinder consensus and impose restrictions on the network topology. We also show that a lower bound on the maximal delay allowable for consensus can be computed by a simple line search method.