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This paper presents a systematic approach to develop a dynamic model for a matrix converter. The matrix converter interfaces two three-phase ac systems that can be at different voltages and/or frequencies, e.g., a high-speed micro-turbine generator and a utility distribution system. The model is developed by (i) transferring the abc frame equations to a newly defined switching reference frame and then (ii) transferring the resultant equations to a rotating dqo frame. The model is then linearized and the concept of "sequential loop closing" is used to design a controller for the matrix converter as a multi-input multi-output system. The accuracy of the developed model and performance of the controller are evaluated based on comparing the study results with those obtained from digital time-domain simulations in the PSCAD/EMTDC software environment.