Consensus Problems for Discrete-time Agents with Communication Delay

In this paper, consensus problems for first-order multi-agent systems with unstable pole are investigated over undirected network, where the network is affected by communication delay. By jointly utilizing both the delayed distributed state information and agent's own historical input information in the protocol, sufficient condition related to agent dynamic, network topology and communication delay is obtained for consensus, which is also proven to be necessary in case of one step delay. Furthermore, the consensus problem is studied on condition that the delay is time-varying. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed theoretical results.