Weighted Group Consensus for Discrete-Time Heterogeneous Multi-Agent Systems in the Cooperative-Competitive Network With Time Delays

Group consensus is investigated for a class of discrete-time heterogeneous multi-agent systems which are composed of first-order and second-order agents with communication and input time delays in this paper. Based on the cooperative-competitive relationship between the agents in the system, a novel weighted group consensus protocol is proposed. Some sufficient conditions are given to guarantee the success of group consensus in some special situations by using z-transformation, matrix analysis and algebraic graph theory. The upper bound of time delays can be reckoned by utilizing Gershgorin disk theorem and generalized Nyquist's criterion. The results show that group consensus has no relationship with communication time delay. Only if the input time delay, the coupling weight between the agents, and the system's control parameters satisfy the given conditions, the multi-agent systems can realize group consensus. Some simulation results show that the proposed novel protocol can effectively promote the multi-agent systems to achieve weighted group consensus.