This paper discusses the robust control of a grid-connected doubly-fed induction generator (DFIG) controlled by vector control using a nonlinear feedback linearization strategy in order to ameliorate the performances of the control and to govern the developed stator active and reactive power in a linear and decoupled manner, in which an optimal operation of the DFIG in subsynchronous operation is given, as well as the control stator power flow with the possibility of keeping stator power factor at a unity. The use of the state-all-flux induction machine model gives place to a simpler control model. So, to achieve this objective, the Lyapunov approach is used associated with a sliding mode control to guarantee the global asymptotical stability and the robustness of the parametric variations.