Finite-Time Couple-Group Consensus for Fractional-Order Multi-Agent Systems with Coopetition Interactions

The problem of finite-time couple-group consensus for fractional-order multi-agent systems with weakly connected topology is investigated in this paper through pinning control. A new error variable based on cooperative and competitive interactions among agents is introduced to transform the fractional-order multi-agent system into a first-order multi-agent system and a novel group consensus protocol is designed for the transformed system. By applying the Lyapunov approach and matrix theory, several sufficient conditions are obtained to ensure the achievement of finite-time couple-group consensus of the system. In addition, the settling time is upper bounded by a definite value, which is independent of the initial states. Finally, the correctness and validity of our findings are verified through some numerical simulations.