Abstract: Hysteresis control technology is a widely used tracking control technology, which has the advantages of fast response speed, no need for modulation stage, simple structure and inherent current limit capability, etc. Hysteresis control has been widely used in inverters and rectifiers, but rarely in matrix converters. The research related to the three-position hysteresis controller and variable band width control is also scarcely reported. Taking into account most of the matrix converter control methods are complex and the computational burden is heavy, the hysteresis control of matrix converter is of great research significance and application potential. This paper mainly focuses on the hysteresis controller of a three-phase direct matrix converter. Firstly, the hysteresis controller based on two-position comparators is designed to control the output currents of the matrix converter. Then the three-position hysteresis controller which is more suitable for the matrix converter is designed considering that the input has three phases. In this way, the choice of voltage selection is increased to three and the control flexibility and accuracy are enhanced. Finally, to address the issues caused by the fixed hysteresis band width in two- and three-position hysteresis controllers, a fuzzy controller is adopted to adjust the band width online, thus improving the control performance. The simulation work is carried out in Matlab/Simulink and simulation results verify the feasibility and effectiveness of the proposed controllers.