The nonlinear induction motor model is appropriately integrated by incorporating the dynamics of the power electronic converter in a manner that permits the design of stable field-oriented control (FOC) operating with minimum losses. As already proven, the challenging issue of operating the induction machine with minimum copper losses requires a varying rotor flux opposed to the standard FOC technique, which keeps the rotor field magnitude constant and tracks the electric torque to the desired level. To this end, exploiting the Hamiltonian structure of the developed motor/converter model, an innovated nonlinear controller is proposed that guarantees the technical limits of the converter (linear modulation) and simultaneously operates under FOC at steady state to achieve accurate speed regulation with varying rotor flux according to the minimal losses requirements. Under these circumstances, the conventional FOC stability analysis does not hold anymore, and therefore for the first time, a new rigorous analysis is provided that proves stability and convergence to the desired equilibrium for the complete closed-loop motor converter system. Finally, the theoretical contribution is examined in comparison to the traditional FOC operation by simulations obtained for an industrial size induction motor, while it is further evaluated by real-time results of a motor with similar parameters.