A systematic controller design and implementation for a matrix-converter-based permanent magnet synchronous motor drive system is proposed. A nonlinear adaptive backstepping controller is proposed to improve the speed and position responses of the permanent magnet synchronous motor system. By using the proposed adaptive backstepping controller, the system can track a time-varying speed command and a time-varying position command well. Moreover, the system has a good load disturbance rejection capability. The realisation of the controller is very simple. All of the control loops, including the current loop, speed loop and position loop, are implemented by a 32-bit TMS320C40 digital signal processor. The hardware circuit is thus very simple. Several experimental results are given to validate the theoretical analysis.