Matrix converters have many advantages including one stage high-efficiency AC/AC energy conversion, bidirectional power flow, a near unity input power factor, sinusoidal three-phase input currents, and sinusoidal three-phase output currents. However, matrix converters cause 360 Hz voltage pulsations at the virtual DC-bus, which increases input current harmonics and output current harmonics. To solve these problems, a systematic design of an input current space-vector modulation method with an input three- phase AC filter is proposed to reduce the input current harmonics. In addition, a predictive current controller is implemented to reduce the current harmonics of the output of the matrix converter, and a predictive speed controller is implemented to improve the dynamic speed responses of the PMSM. A digital signal processor, manufactured by Renesas Electronics Corporation with a type SH7237, and an FPGA, manufactured by Intel Corporation with a type 10M16SAU16917G, are used to execute the control algorithms. Several experimental results validate the theoretical analysis.