Consensus in the network with uniform constant communication delay

This paper studies consensus among identical agents that are at most critically unstable and coupled through networks with uniform constant communication delay. An upper bound for delay tolerance is obtained which explicitly depends on agent dynamics and network topology. The dependence on network topology disappears in the case of undirected networks. For any delay satisfying this upper bound, a controller design methodology without exact knowledge of the network topology is proposed so that multi-agent consensus in a set of unknown networks can be achieved. Moreover, when the network topology is known, a larger delay tolerance is possible via a topology-dependent consensus controller.