Quasi-Consensus of Fractional-Order Multi-Agent Systems with Mixed Delays and External Disturbance via Impulsive Pinning Control

In this brief, the quasi-consensus issue is examined for fractional-order multi-agent systems (FROMASs) subject to both mixed delays and external disturbances, employing an impulsive pinning control (IPC) strategy. Unlike mainstream pinning strategies with fixed nodes or static rules, a dynamic pinning mechanism based on consensus error distances is proposed, which adaptively adjusts the set of pinned nodes at each impulsive instant. By integrating the Razumikhin method, Lyapunov stability theory, and the comparison system approach, sufficient conditions for achieving quasi-consensus of FROMASs are established. Moreover, the convergence bound of consensus errors is quantitatively estimated and shown to be explicitly determined by the intensity of external disturbances. This paper organically integrates the dynamic node pinning mechanism, FRO impulsive control, and Razumikhin stability analysis. It effectively handles mixed delays and external disturbances while significantly reducing control costs. Finally, numerical simulations show that the synchronization errors are strictly bounded within the threshold M=13.6372, which effectively validates both the proposed control scheme and the theoretical analysis.