An adaptive observer for rotor resistance is designed to estimate rotor flux for the a-b model of an induction motor assuming that rotor speed and stator currents are measurable. A singularly perturbed model of the motor is used to design an Adaptive sliding mode observer which drives the estimated stator currents to their true values in the fast time scale. The adaptive observer on the sliding surface is based on the equivalent switching vector and both the estimated fluxes and the estimated rotor resistance converge to their true values. A speed controller considering the effects of parameter variations and external disturbance is proposed in this paper. First, induction motor dynamic model at nominal case is estimated. based on the estimated model, speed controller is designed to match the prescribed speed tracking specifications. Then a dead-time compensator and a robust controller are designed to reduce the effects of parameter variations and external disturbances. the desired speed tracking control performance can be preserved under wide operating range, and good speed load regulating performance. Some simulated results are provided to demonstrate the effectiveness of the Proposed controller.