This paper proposes a self-scheduled control method for a doubly-fed induction generator driven by a wind turbine (DFIGWT), whose rotor is connected to the power grid via two back-to-back PWM power converters. We design a controller for this system using the linear matrix inequality (LMI) based approach to linear parameter varying (LPV) systems, which takes into account the nonlinear dynamics of the system. We propose a two-loop hierarchical control structure. The inner-loop current controller, which considers the slip frequency as a variable parameter, achieves robust tracking of the rotor current reference signals. The outer-loop electrical torque controller aims for wind energy capture maximization and generates the reference rotor current. We perform a controller reduction for the inner-loop LPV controller, which is not doable by conventional model-reduction techniques, because the controller is parameter-dependent. In simulation, the reduced order controller has been tested on a nonlinear 5th order DFIGWT model. Stability and high performances have been achieved over the entire operating range of the DFIGWT