The present article proposes a nonlinear optimal control method for magnetically geared induction motors. It is proven that the dynamic model of the magnetically geared three-phase induction motor is differentially flat, which confirms the controllability of this system. Next, to apply the nonlinear optimal control scheme the dynamic model of the magnetically geared motor undergoes approximate linearization with the use of first-order Taylor-series expansion and through the computation of the associated Jacobian matrices. For the approximately linearized model of the magnetically geared induction motor an H-infinity optimal feedback controller is designed. To compute the controller's stabilizing feedback gains an algebraic Riccati equation has to be solved repetitively at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control scheme are proven through Lyapunov analysis.