In this article, a nonlinear optimal control approach is developed for voltage-source inverter-fed six-phase Permanent Magnet Synchronous Motors which can be used in electric vehicles' traction. The dynamic model of the VSI-fed six-phase PMSM undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization is based on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis.