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Stability and good dynamic performances of adaptive full-order observers are of utmost importance for the sensorless PMSM drive. In this paper, to accomplish both requirements, the analytical stability conditions are firstly derived to provide a general framework for the feedback gain design. Closed-form solutions of the stabilizing feedback gains are consequently given, and are used in the zero and pole placement design to obtain an adequate and constant damping factor along with the stability at all operating frequencies. New design rules for the adaptation of PI gains to satisfy the required performances are also proposed. The robustness of the adaptive full-order observer against stator resistance and inductance variations is also investigated. Validity of the designed sensorless control is confirmed by simulation and experiment.