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This paper reports on the modeling and control of a flywheel energy storage system used for electric vehicle. First, by the experimental vibration analysis based on the rigid model with H-infinity control, it was found that the main cause of the flywheel rotor instability due to the influence of the first bending backward mode than that of gyroscopic effect. Subsequently, a flexible model was derived using the finite-element method and a mode separation method using the singular value decomposition was proposed for the gyroscopic matrix in order to obtain the reduced-order model. The effectiveness of the reduced-order flexible model and that of H-infinity controller were verified by the simulation.