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While the known modulation and control techniques for four-leg matrix converters are based on pulse width modulation or three-dimensional space vector modulation, this paper presents a simple current control strategy based on prediction calculation to select the switching states of the converter. By using a predictive cost function, the optimal switching state to be applied to the next sampling time is selected. This is done in order to minimize the instantaneous reactive power on the input side and to obtain a positive dc-link voltage at any time, while maintaining a good tracking of the load currents to their respective references. The feasibility of the proposed strategy is verified by simulation results.