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Rotating stall and surge are aerodynamic instabilities that limit the performance of aeroengines. A set of magnetic bearings supporting the compressor rotor is a potential actuator for active control of rotating stall and surge. Based on a first-principles model we show that using this type of actuation, the first harmonic mode of rotating stall is linearly controllable, but the second harmonic mode and the surge mode are linearly uncontrollable. We then give an explicit procedure for designing feedback laws such that the first mode is linearly stabilized and the criticality of the Hopf bifurcations of the second mode and the surge mode are supercritical. We also investigate the effects of magnitude saturation on the regions of attraction. We demonstrate the theoretical results by numerical simulations of a model for a transonic compressor at the NASA Lewis Research Center.