This paper presents a new control method for a matrix-converter-based induction machine drive. A discrete model of the converter, motor, and input ﬁlter is used to predict the behaviour of torque, ﬂux, and input power to the drive. The switching state that optimizes the value of a quality function, used as the evaluation criterion, is selected and applied during the next discrete-time interval. Experimental results conﬁrm that the proposed strategy gives high-quality control of the torque, ﬂux, and power factor with a fast dynamic control response. The key implementation issues are analyzed in depth to give an overview of the realization aspects of the proposed algorithm. The method has a fast torque response, unity PF with low reactive power delivered to the mains, and low torque and ﬂux ripple. The objectives of this paper are to introduce the method and its theoretical background, analyzing, in depth, the most relevant issues related to its implementation and showing its excellent performance based on experimental results.