A matrix converter includes a plurality of switching elements and is adapted to receive a multi-phase alternating current (AC) input signal having an input frequency and to generate a multi-phase AC output signal having an output frequency. The phases of the input signal are sorted as a function of their instantaneous voltage amplitude (60). A reference signal is generated from output reference voltages that correspond to each phase of the output signal (56). Duty cycles are calculated for each phase of the output signal based on the sorted input signal phases and the reference signal (62). Switching functions, which each control one of the switching elements, are then generated based on the duty cycles for each phase of the output signal (64, 66).