This work investigates the problem of speed sensorless state estimation for induction motors. We first exploit a state transformation for the induction motor model. Based on the new state coordinates, we design a new Luenberger observer, which can provide better dynamic performance compared to baseline algorithm. To address the parameter variation problem, the Lyapunov redesign method is used to achieve an adaptation with respect to the parameter α. It is shown that the proposed observer can achieve guaranteed asymptotic stability and readily extend to the time-varying speed case. Advantages of the proposed observer include guaranteed asymptotic stability of estimation errors, parameter a adaptation, and better dynamic performance. Simulation results are presented to validate the proposed method.