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A matrix converter is a direct ac/ac power converter with sinusoidal input currents and no bulky de-link capacitor. With these features, it offers remarkable advantages over other alternatives in applications requiring improved utility interaction and critical weight/volume reduction. Lately, the indirect matrix converter topologies have been investigated, leading to a possibility of a reduced switch number and a multi-drive application. However, due to off-line input current regulations of the matrix converter, input displacement power factor varies with the LC input filter and load condition. This fact yields non-unity displacement power factor and increased switching losses. In this paper, a novel on-line input current control strategy is proposed based on a closed-loop control in the synchronous reference frame. The approach allows independent control of the two input current components (active and reactive), yielding zero reactive components. In addition, this paper shows the indirect matrix converter has minimum switching losses with the input currents in phase with the input voltages by specifying a relationship of input current phase angle and the switching losses in semiconductors. Simulation results are presented for the feasibility of the proposed technique and the experimental results are in progress.