Consensus of Multi-agent System with Diverse Communication Delays

In this paper, a protocol is proposed to solve the consensus problem of multi-agent system with diverse communication delays. Sufficient conditions for the convergence to a consensus are obtained based on the frequency-domain analysis and matrix theory. The conditions depend on each agent's self-delay, the weights of the edges to each agent's neighbors, and the interconnection topology of the network. Under the proposed protocol, introducing self-delay can speed up the convergence rate for the system with communication delays. Moreover, the communication delays do not influence the convergence; they prolong the converging time instead. Simulation results illustrate the correctness of the results.