Bounds on Delay Margin for Consensus of General Second-Order Multi-Agent Systems

This paper studies the delay margin and its bounds for second-order multi-agent systems to achieve robust consensus with respect to uncertain delays varying within a range. The issue under investigation dwells on the question: What is the largest delay range within which a distributed control protocol is able to achieve and maintain the consensus? We consider second-order agents with real unstable poles communicating over an undirected network topology, and derive bounds on the delay margin. The results show that for a strictly unstable second-order multi-agent system, its consensuability robustness depends on the pole locations of the agents, as well as on the eigen-ratio of the network graph.