This paper describes the design of a new algorithm for the rotor resistance adaptation. The obtained adaptive observer is used for the improvement of the vector control of induction motor (IM) drives. The adaptive observer detects the rotor speed and flux components in the stationary reference frame using the stator voltages and currents. Stability analysis based on Lyapunov theory is performed in order to guarantee the closed loop stability. In addition, the estimated rotor resistance is used for correction of the controllers and the rotor time constant which is used in the calculation of the stator pulsation. Simulation tests under disturbances are provided to evaluate the consistency and the effectiveness of the proposed control technique in terms of robustness and dynamic performances.