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This paper presents a sensorless speed control for a permanent magnet synchronous motor (PMSM) combining a robust backstepping controller and a sliding mode observer based on the super twisting algorithm. Firstly, the structural property of the observability of this machine is analyzed. Then, an observer is designed in order to estimate the speed and the position of the machine from the only measurement of the currents and the voltages. A robust backstepping controller is then designed in order to track a desired speed reference under uncertainties and unmodeled dynamics. The result is obtained in spite of uncertainties in the stator resistance and stator inductance, which usually are bad known and time-varying. Simulation results are shown in the framework of an industrial benchmark to illustrate the performance of the proposed scheme with the critical case of standstill and low speed.