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This study systematically analyzes multilevel space-vector pulse width modulation for a multiphase voltage source inverter (VSI). The instantaneous output voltages of the VSI, which are called space vectors, can be classified according to the switching states of the VSI. By applying the eigenspace decomposition of the system matrix, the n-phase VSI control problem can be solved analytically. This analysis leads to a switching strategy that uses the fewest space vectors and minimum total conduction time. This yields a minimum switching number and efficient dc supply utilization. Further, the switching strategy of a multilevel multiphase VSI system can be solved based on the switching strategy of a two-level multiphase VSI. Simulations and experimental results confirm the effectiveness of the proposed algorithm.