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The development of robust controllers for high-speed flywheel rotors supported on active magnetic bearings (AMBs) has been extensively studied over the past decade. Such flywheels can be used as energy momentum wheels (EMWs) onboard spacecraft, and pose a challenging control problem due to their high flexibility, nontrivial parametric uncertainty, and rotor-speed dependence. A combined H∞ loop shaping and μ-synthesis approach is used in this paper to design controllers for EMWs supported on AMBs. This combination between these two well-established control methodologies is novel to the design of robust controllers for such systems. H∞ loop shaping guarantees (through the specification of loop-shaping weights) closed-loop performance and robustness to generic unstructured coprime factor uncertainty, whereas robustness to highly directional parametric uncertainty is incorporated through a μ-synthesis design. Furthermore, in order to reduce the computational complexity of the control design and the order of the synthesized controllers, a method is proposed in this paper to reduce the number of states that depend on the rotor speed. The proposed methodology is demonstrated through numerical simulations and experimental results.