Speed-adaptive full-order flux observer becomes unstable during regenerating operation at low speed. The instability problem is caused by inappropriate designing of observer. Based on the eigenvalues of extended observer, this paper interprets unstable situation, that the eigenvalues of extended observer have a positive real part. The method based on the eigenvalue gives the complete stability condition for speed adaptive full order observer, which is used to stabilize observer. The observer designed using proposed method was verified in the torque controlling application of 20kW induction motor.