In this paper, the weighted couple-group consensus of continuous-time heterogeneous multiagent systems with input and communication time delay is investigated. A novel weighted couple-group consensus protocol based on cooperation and competition interaction is designed, which can relax the in-degree balance condition. By using graph theory, general Nyquist criterion and Gerschgorin disc theorem, the time delay upper limit that the system may allow is obtained. The conclusions indicate that there is no relationship between weighted couple-group consensus and communication time delay. When the agents input time delay, the coupling weight between the agents, and the systems control parameters are satisfied, the multiagent system can converge to any given weighted coupling group consistent state. The experimental simulation results verify the correctness of the conclusion.

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. INDEX TERMS Weighted group consensus, cooperative-competitive network, discrete-time, heterogeneous multi-agent systems, time delays.

In this paper, the weighted couple-group consensus is investigated for a kind of continuous heterogeneous multi-agent systems in the cooperation-competition networks with time-delay. A novel weighted couple-group consensus protocol is proposed on basis of self-adaptive and cooperative-competitive mechanism. In this novel couple-group control protocol, self-adaptive regulation, weighted-distribution, cooperation-competition, position and velocity are considered. By applying the graph theory, complex frequency analysis method and linear algebra theory, some sufficient conditions have been given to guard the success of the couple-group consensus for this kind of heterogeneous multi-agent systems. Furthermore, the upper limit of the time delay may be computed if the weighted parameters are determined. The results show that the multi-agent system can converge to couple-group consensus state only if the upper bound input time-delay is satisfied the given time span. Some simulation examples show the validity of the obtained results. LI REN is currently pursuing the degree with the School of Automation, Chongqing University of Posts and Telecommunications, Chongqing, China. His current research interest are the group consensus of multiagent systems with switching topologies systems, and intelligent algorithms. CHAOWEN XIONG is currently pursuing the degree with the

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