Resolvers are absolute angle transducers that are usually used for position and speed measurement in permanent magnet motors. An observer that uses the sinusoidal signals of the resolver for this measurement is called an Angle Tracking Observer (ATO). Current designs for such observers are not stable in high acceleration and high-speed applications. This paper introduces a novel hybrid scheme for ATO design, in which a closed-loop LTI observer is combined with a quadrature encoder. Finite gain stability of the proposed design is proven based on the circle theorem in input-output stability theory. Simulation results show that the proposed ATO design is stable in two cases where an LTI observer and an extended Kalman filter are unstable due to high speed and acceleration,. In addition, the tracking accuracy of our hybrid scheme is substantially higher than a single quadrature encoder.