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This paper presents a new speed and position sensorless control method of permanent magnet synchronous motors based on the sliding mode observer. The sliding mode observer structure and its design method are described. Also, Lyapunov functions are chosen for determining the adaptive law for the speed and the stator resistance estimator. The effectiveness of the proposed observer is confirmed by the experimental results.Index Terms-PMSM (Permanent magnet synchronous motor), sensorless control, sliding mode control, stator resistance estimation.