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A nonlinear robust control design for the levitation and propulsion of a magnetic levitation (maglev) system is presented. The maglev dynamics under consideration are nonlinear and contain uncertain dynamics including negative damping due to eddy currents. The proposed recursive controller is designed using nonlinear state transformation and Lyapunov's direct method in order to guarantee global stability for the nonlinear maglev system. Simulation results are provided to show the effectiveness of the proposed control design.