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 This paper presents a novel Z-source Sparse Matrix Converter (ZSMC) and its fuzzy logic controller based compensation method under unbalanced input voltage conditions. The ZSMC is developed based on the structure of a sparse matrix converter (SMC) to reduce the number of unipolar power semiconductor switches and employs a Z-source network to overcome the inherent limitation of the low voltage transfer ratio of the conventional matrix converters. Although the ZSMC is a two-stage converter, it directly connects between a source and a load without any intermediate energy storage component at the dc-link except the Z-source network for the boosting purpose. Therefore, the output of the ZSMC is directly affected by the disturbance in the input voltage source. In this paper, the topology and operational principle of the ZSMC is described and its modulation strategy is explained. A compensation method, based on a fuzzy logic controller, is presented to improve the output performance of the ZSMC under unbalanced input voltage conditions. The simulation and experimental results are shown to verify the feasibility of the ZSMC and its compensation method.