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The Commutation strategy of matrix converters for high-frequency unity power factor applications has been a challenge for years. The strategy should be simple, have a short duration, and possibly avoid current sensing. This paper proposes a new strategy for the bidirectional switch commutation of the three-phase to two-phase matrix converters supplying inductive power transfer (IPT) systems. This strategy's main merits are simplicity, the reduction of commutation time, and no need for detecting the load current sign, which is crucial for synthesizing the output voltage accurately. Pulse density modulation is used because of the high frequency output voltage and possibility of utilizing three phases in any particular output cycle leading sinusoidal shape of grid current. Presented simulation and experimental results verify the converter's appropriate function using the proposed strategy and a reduced switching state machine.