Consensus of first-order agents with time-varying communication delay

In this paper, we consider the consensus problems for first-order multi-agent systems with communication delay. Under the assumption that the delay is time-varying and unknown, allowable delay bound depending on agent dynamic, control gain and the eigenvalues of the Laplacian matrix are obtained over undirected network topology. Especially, if the agent dynamics are first-order integrator systems, any large and bounded communication delay is allowed for consensus. Finally, a numerical example is given to validate the theoretical results.