Weighted Group Consensus Analysis of Multi-agent Networks with Different Time Delays

For first-order multi-agent systems with connected bipartite topology, this paper investigates the weighted group consensus problem of the systems with different time delays. By applying the frequency domain control theory, we analyze and obtain the sufficient condition such that the systems can reach weighted group consensus. The obtained conclusions show that the achievement of the systems' group consensus relates to the weights between the agents and the input time delays of the agents, while communication time delays between the agents are irrelevant to it. However, communication time delays will affect the dynamic performance of the systems. When the communication time delays of the systems satisfy the assumption proposed in this paper, the weighted group consensus of the system can be reached. Finally, several simulations show the correctness of the obtained results.