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This paper explores a robust μ-synthesis control scheme for structural resonance vibration suppression of high-speed rotor systems supported by active magnetic bearings (AMBs) in the magnetically suspended double-gimbal control moment gyro (MSDGCMG). The derivation of a nominal linearized model about an operating point was presented. Sine sweep test was conducted on each component of AMB control system to obtain parameter variations and high-frequency unmodeled dynamics, including the structural resonance modes. A fictitious uncertainty block was introduced to represent the performance requirements for the augmented system. Finally, D-K iteration procedure was employed to solve the robust μ-controller. Rotor run-up experiments on the originally developed MSDGCMG prototype show that the designed μ-controller has a good performance for vibration rejection of structural resonance mode with the excitation of coupling torques. Further investigations indicate that the proposed method can also ensure the robust stability and performance of high-speed rotor system subject to the reaction of a large gyro torque.