We describe the automatic synthesis of a global nonlinear controller for stabilizing a magnetic levitation system a simplified model for the German Transrapid system. A systematic state-space design method for determining the global switching points of the controller is presented. The synthesized control system can stabilize the maglev vehicle with large initial displacements from an equilibrium, and possesses a much larger operating region than the classical linear feedback design for the same system. The controller is automatically synthesized by a suite of computational tools that visualize and model the state-space geometry and topology of a given system, use a novel technique of 'flow pipes' to plan global reference trajectories in state space, and navigate the system along the planned trajectories. Magnetic levitation, Control system synthesis, State-space methods, Artificial intelligence, Computer-aided design, Numeric/symbolic processing.