Couple-group consensus of heterogeneous fractional Multi-Agent Systems with pinning and self-adaptive controller

In this paper, the couple-group consensus for a kind of heterogeneous fractional multi-agent systems (HFMASs) with time-varying delay has been investigated. Based on cooperative-competitive interactions, a novel consensus protocol has been proposed for this kind of HFMASs. Furthermore, the pinning controller and self-adaptive controller have been introduced into this control protocol. By using Lyapunov function and linear matrix inequality (LMI) technology, some sufficient conditions have been obtained for the couple-group consensus of this system. Finally, some simulation examples have been given to prove the validity of these conclusions.