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This paper discusses the couple-group consensus problems for a class of heterogeneous multiagent networks including the following two cases: with communication and input time delays, respectively. Different from the related cooperative networks, two novel delayed group consensus protocols are designed based on the competitive relationship between the agents. Furthermore, we absolutely relax the in-degree balance and other restrictive preconditions which existed in the relevant works. Some sufficient algebraic criteria for the achievement of couple-group consensus and the upper bound of the input time delays are technically obtained via the frequency domain method and matrix theory, respectively. The results show that the achievement of the couple-group consensus depends on the second-order agents’ in-degree and the control parameters of the systems, whereas it is independent of the communication time delays. Meanwhile, the upper bound of the input time delay is determined by the control parameters and the in-degree of the first-order agents. Finally, the validity of the proposed results is verified by several simulated examples

Heterogeneous and Competitive Multiagent Networks: Couple-Group Consensus with Communication or Input Time Delays