Group Consensus Analysis of Multi-agent Systems with Cooperative-Competitive Interactions and Time Delays

This paper mainly studies the group consensus problem of multi-agent systems under the influence of different input and communication time delays. Based on the principle of competition and cooperation among agents, group consensus control protocols are designed for the first and second order multi -agent systems that agents are connected by a directed communication network. By using the knowledge of frequency domain control theory, the sufficient conditions for group consensus of multi -agent systems are obtained. It is found that the coupling weight between agents, the input time delay of each agent and the control parameters in the controller all affect the realization of group consensus of the multi -agent systems. The communication delays among agents do not affect the final convergence of the systems, but the communication delay will affect the dynamic performance of the systems. The research shows that the smaller the time delay, the faster the system can achieve asymptotic stability. Numerical simulation results verify the correctness of the conclusion.