Synchronization in a network of identical continuous- or discrete-time agents with unknown nonuniform constant input delay

This paper studies the synchronization problem for multiagent systems with identical continuous- or discrete-time agents with unknown nonuniform constant input delays. The agents are connected via full- or partial-state coupling. The agents are assumed to be asymptotically null controllable, ie, all eigenvalues are in the closed left-half complex plane for continuous-time agents or in the closed unit disc for discrete-time agents. We derive an upper bound for the input delay tolerance, which explicitly depends on the agent dynamics. Moreover, for any unknown delay satisfying this upper bound, a low-gain–based protocol design methodology is proposed without relying on exact knowledge of the network topology such that synchronization is achieved among agents for any network graph in a given set.