The DC power system of more electric aircraft (MEA) features low inertia and limited capacity, making it vulnerable to bus voltage fluctuations from pulsed power loads. The hybrid power supply system (HPSS) efficiently meets the demands of supplying and absorbing transient pulsed power. However, its application in airborne systems is challenged by the multi-time-scale dynamics of power sources and loads, as well as complex and variable flight conditions, making reliable and coordinated power distribution difficult. In this article, a decentralized power stabilization strategy based on virtual impedance matching is proposed, incorporating virtual inductance, resistance, and capacitance into the droop control of fuel cell, lithium battery, and supercapacitor units, respectively. The strategy enables automatic frequency-based power sharing, maintains bus voltage stability under dynamic conditions and source failures, and supports regenerative energy recovery. The simulation results verify the accuracy and effectiveness of the proposed method.