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Multilevel converters and, in particular, flying capacitor (FC) converters are an attractive alternative for medium-voltage applications. FC converters do not need complex transformers to obtain the DC-link voltage and also present good robustness properties, when operating under internal fault conditions. Unfortunately, with standard modulation strategies, to increase the number of output voltage levels of FC converters, it is necessary to increase the number of cells and, hence, the number of capacitors and switches. In this paper, we develop a finite-state model predictive control strategy for FC converters. Our method controls output currents and voltages and also the FC voltage ratios. This allows one to increase the number of output voltage levels, even at high power factor load conditions and without having to increase the number of capacitors and switches. Experimental results illustrate that the proposed algorithm is capable of achieving good performance, despite possible parameter mismatch.