On pinning couple-group consensus for cooperative-competitive heterogeneous multi-agent systems with Markov switching topology

Abstract

The paper investigates the control problem of pinning couple-group consensus for heterogeneous multi-agent systems with the Markov switching topology. A novel protocol of group consensus is designed based on the cooperative-competitive relationship among the agents. By means of the algebraic graph theory, Lyapunov stability theory, matrix theory as well as continuous Markov process analysis, several sufficient conditions and pinning control strategy are presented for the realization of group consensus of the system with connected components topology. Besides, we find that the in-degree of the agents, the control parameters of the system and the pinning gains of the second -order agents are closely related to the achievement of couple-group consensus. Finally, the correctness of the theoretical results is verified by simulation experiments.