This paper deals with the stability analysis and the active stabilization of Voltage-Source-Rectifier Loads in AC microgrids using a centralized stabilizer. A model of this system is first performed considering the voltage loop dynamics of the rectifier and stability analysis is done using the indirect method of Lyapunov. The stabilizability study realized with Lie algebra shows that the action of an external stabilizer is limited to the AC side of the system. This stabilizer is an inverter only dedicated to the stabilization of the AC bus of the system at the connecting point. To improve the stability area, a feedback control of the stabilizer based on the small-signal theory is developed. A theoretical analysis, simulations and experimental results are presented to evaluate the effectiveness of the proposed method.