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While the matrix converter has many advantages that include bidirectional power flow, a size reduction, a long lifetime, and sinusoidal input currents, it is vulnerable to the input voltage disturbances, because it directly exchanges the input voltage to the output voltage. The instantaneous effective power control (IEPC) method has been proposed to compensate the input voltage disturbances, in which the instantaneous effective power is kept constant by controlling input current. However, to date, no method has been proposed to maintain the stability of the system with the IEPC. The purpose of this paper is to propose a method to control the stability of the system with IEPC. First, this paper explains the IEPC theoretically. Next, a model of the system with the IEPC is developed, and stability analyses are conducted. Then, based on the results of the analyses, a stability control method for the system with the IEPC is proposed. Furthermore, the validities of the proposed method are demonstrated by simulation and experiments. Finally, a restart performance of the system after momentary power interruption is discussed. Because the IEPC does not need phase-locked-loop to detect the phase angle of the input voltage, fast restart is expected. Index Terms--Instantaneous effective power control (IEPC) method.