Consensus realization for discrete‐time multi‐agent systems with delayed information

Abstract This manuscript mainly addresses the consensus problem for first‐order multi‐agent systems over an undirected graph. The study considers unstable systems, where the communication delay affects only the neighbors' information. A distributed control protocol incorporating delayed information is proposed. Using the Jury stability criterion in the frequency domain, a necessary and sufficient condition for consensus under one‐step delay is established. Additionally, time‐domain techniques are employed to obtain sufficient conditions for consensus under any large yet bounded delay, which may be unknown and time‐varying. Furthermore, the results of the scalar case are extended to high‐order agent dynamics with a single unstable pole. Finally, three numerical examples are presented to verify the effectiveness of the proposed results.