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This paper investigates the multi-group consensus problem for heterogeneous networks via pinning control and adaptive coupling weight methods. In view of the network's topology with connected components, the cooperative–competitive interactions among the agents and Markov switching topology are considered. Based on Lyapunov stability theory and algebraic graph theory, several sufficient conditions and pinning control strategies are presented to guarantee the network reach multi-group consensus. The results reveal that the in-degree of the agents and pinning gains of the second-order agents are closely related to the achievement of multi-group consensus. Finally, simulation experiments are given to verify the correctness of the theoretical results. Moreover, the simulated results show that the adaptive coupling weight method can increase the convergence rate of the network.

Multi-group consensus for heterogeneous agents in cooperative–competitive networks via pinning and adaptive coupling weight methods