Abstarct: In recent years, matrix converters because of the vast benefits have been paid special attention. Among these advantages Adjustable input unit power factor, power transfer in both directions and form waves with a very high quality input and output, and also due to the absence of elements such as energy storage capacitors in the DC bus converters' matrix the possibility of making them into a compact circuit and there are small but. However, due to problems such as complex commutation complex circuit protection against voltage added, using the direct matrix converters in the industry until recently has been postponed. On the other hand, the ability to restore energy by the matrix converter, it is possible that more kinetic energy at the source to be returned in this case only the losses due to switch input is filtered as a result of using this converter in the drive Induction motors with high efficiency will be achieved. Unlike the three-phase matrix converter three-phase and three phase matrix converter single phase to three phase matrix converter in phase two work less has been done so that this project, all states that can be the matrix converter, two-phase voltage produced, States that this is designed as two conventional three-phase matrix (direct) and indirect are. Each of these converters as well as two state and two tripod baxse design and methods of switching each one separately is also given. Due to losses in switching converters, high model with switches declined to reduce the switching losses is given so that the converter Rectifier side (the line) only three switches are used. Simulixnk MATLAB environment as a two-phase induction machine simulation and design of matrix converters for induction motor speed control system.