This paper presents a Linear Parameter-Varying (LPV) observer for an Induction Machine (IM) under sinusoidal DC-supply disturbances. The observer estimates not only the IM state variables, but also the disturbances considered as a part of the states. As the extended IM model depends on the stator angular speed and the rotor angular speed , the proposed observer is designed by convex optimization to induce a convergence of the observer for a predetermined range of and . The estimated disturbances can be used to compensate for the real disturbances. The simulation results show the effectiveness of the observer, and experimental results on a laboratory test-bench have been obtained. The proposed method can be extended to other type of motor drives.