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Design strategy of both feedback gains and adaptation gains for an adaptive full-order observer is a necessary issue to assure the stability and the tracking performance of the speed estimation in the sensorless drives. In this paper, novel design of feedback gains of the observer is proposed to achieve the stability over the whole operation especially in the low-speed region, including the regenerating mode. Stability improvement using the proposed feedback gains is rigorously proven by the method of Lyapunov. For the adaptation proportional-integral (PI) gains, the ramp response characteristic of the speed estimator is proposed as design guidelines. It is revealed that the integral adaptation gain determines the tracking error of the speed estimator during acceleration/deceleration while the sensitivity to current measurement noises depends on the proportional adaptation gain. It is also pointed out that a suitable corner frequency of the adaptation PI gains is required as a design tradeoff to avoid an oscillation. The validity of all theoretical results is verified by simulation and experiment.