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In this paper, couple-group consensus is investigated for a kind of heterogeneous multi-agent systems (HMASs) with Markov switching. Some novel couple-group consensuses have been proposed, in which cooperative-competitive interaction, Markov switching and time delay are all considered. For Markov switching, the transitive rate of probability can be divided into two cases: known or partly known. Based on stochastic delta operator, probability, graph and stability theories, the leader-following and pinning couple-group consensus of this system be converted into analyzing the stability of related switching delta operator system. In the obtained results, some conservative conditions, such as the balance of in or out degree, strong connectivity and containing a spanning tree, can be longer strictly demanded. Some numerical examples are given to show the validity of the acquired results.

Couple-Group Consensus of Heterogeneous Multi-Agents Systems With Markov Switching and Cooperative-Competitive Interaction