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This paper presents an analysis by which the stability of a multiple-input-multiple-output system of simultaneous speed and stator resistance estimators for sensorless induction motor drives can be successfully predicted. The instability problem of an adaptive flux observer (AFO) is deeply investigated. In order to achieve stability over a wide range of operation, a design of the observer feedback gain is proposed. Furthermore, closed-loop control systems of the independent use of the two estimators are developed. Therefore, all gains of the adaptive proportional-integral controllers are selected and generalized to provide good tracking performance as well as fast dynamic response. The performance of the AFO using the proposed gains, with a sensorless indirect-field-oriented-controlled induction motor drive, is verified by simulation and experimental results. The results show a good improvement in both convergence and stability, particularly in the regenerative mode at low speeds, which confirm the validity of the proposed analysis.