This paper shows that it is possible to extend the principle of field-oriented control (FOC) approach to a double-star induction motor (DSIM). In the first stage, a robust variable structure current controller based on space phasor voltages PWM scheme is established. In this current controller design, only the stator currents and rotor speed sensors are used. In the second stage, the FOC method developed for DSIM is motivated by the minimization of the copper losses. The developed approach uses a loss model controller (LMC) and an adaptive rotor flux observer to compute the adequate rotor flux value minimizing the copper losses. The control variables are the stator currents or the machine input power. Compared to the constant rotor flux approach, it is proved that higher performances are achieved. However, the sensitivity of the FOC to parameter error of the machine still remains a problem. To guarantee the performance of the vector control, the stator and rotor resistances are adapted on-line, based on the Lyapunov theory. An appropriate choice of the reference model allows building a Lyapunov function by means of which the updating law can be found. The simulation results show the satisfactory behaviour of the proposed identification algorithm.