AbstractOne of the representative vector‐controlled induction motor drive systems without a speed sensor is composed of a rotor flux estimator, a PI torque current controller and a conventional vector‐controlled current source. However, the stability analysis of this system has not been reported.In this paper, the flux estimator is interpreted as a flux observer. Then a linear model of the system is proposed by deriving the equations of the flux estimator in a synchronously rotating reference frame. By computing the trajectories of the poles and zeros and the transient responses, the following results are obtained.(1) If the rotor flux is estimated using only the stator equations (voltage model), the system becomes unstable when the actuator stator resistance is smaller than the value used by the controller.(2) By choosing a small time constant of the first‐order lag element in the flux estimator (reciprocal number of observer gain), the poles and zeros on the imaginary axis move to the stable region. However, another pair of poles has reverse performance.(3) From the viewpoint of stability, the gain of the PI torque current controller should be chosen as large as possible and the stator and rotor resistances in the controller should be set to values smaller than their actual v