This paper is concerned with the design of a self-scheduled current controller for doubly fed induction machines. The design is based on the framework of linear parameter-varying systems where the mechanical angular speed is considered to be a measurable time-varying parameter. The objective is to obtain robust dynamic performance for all variations of the mechanical rotor speed in a specified operating range. Employing the benefits of digital control, a continuous-to-discrete time transformation is utilized to replace the continuous-time current controller by an approximating discrete-time controller. Experimental results are provided to demonstrate the performance and robustness of the controlled system with respect to changes of the mechanical rotor speed and against stator voltage dips.