Distributed Consensus for High-order Agent Dynamics with Communication Delay

In this paper, consensus problem for high-order multi-agent systems that are at most critically unstable is researched under directed graph. Under the assumption that the delay appears in the communication and being unknown, a distributed protocol with delayed relative state information is proposed to solve the problem, and the design of the constant control gain is not utilizing the precise information of delay. If the agent dynamics has nonzero poles on the imaginary axis, an allowable delay bound is provided to guarantee consensus by studying the joint effects of agent dynamics, network topology and communication delay; otherwise, consensus is tolerant for any large yet bounded communication delay. Especially, it is shown that the unknown delay in communication is allowed to be time-varying if the network topology is undirected, and in this case the delay bound can be enlarged by improving the synchronizability of the undirected graph. ^Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical result.