In this paper, a scalable, plug-and-play (PnP) and system-stable synthesis control method is proposed for the AC island microgrid consisting of a distributed generator unit (DGU) and loads connected by power lines. The proposed method only requires a limited global parameter design controller, so the design process of the controller is decentralized, so that the addition and removal of DGU only need to adjust the controller of the DGU with its physical connection, without affecting the overall stability of the microgrid. In addition, we used the Lyapunov method to proved the stability of the close-loop system. Finally, the simulation verification was carried out with the MATLAB/Simulink and specific cases.