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In speed sensorless induction machine control, the reduced-order observer, i.e., the combined voltage and current (UI) mode flux observer, obtains good flux estimation results in the full-speed range but has some drawbacks in the stability characteristics. This paper constructs the small-signal model of the UI mode flux observer and derives the characteristic matrix to realize the stability analysis, based on which the stable range with corresponding conditions has been calculated explicitly. Furthermore, a cross-coupling feedback mechanism is proposed to solve the instability problem when the machine runs in the low-speed regenerating or plugging-in mode. The cross-coupling feedback coefficient is adjusted by the estimated speed or the speed command (conditional) for further simplification and is easy to be implemented. The improvement strategy is well verified by both the simulation in MATLAB and corresponding experimental results. [ABSTRACT FROM AUTHOR]