The linear control of doubly-fed induction machines in wind power systems normally encounters the problems in variations of the rotor mechanical angular speed and other time-varying parameters. However, better performance requirements against changes in the machine parameters and exogenous inputs are desired. This can be achieved by appropriate controller design. Furthermore, the robustness of the controlled system under the effects of grid voltage dips is an important aspect as well. This work focuses on the use of linear matrix inequalities for analysis and synthesis of current controllers for doubly fed induction machines in wind power systems. The design is aimed at improving the robust dynamic performance of the controlled system in a wide range of mechanical rotor speed variations and reducing the effect of stator voltage dips when the grid undergoes a fault. A rigorous robust analysis based on the integral quadratic constraints approach is presented for evaluating and comparing the robustness of the controlled system with respect to the changes in the machine inductances and the rotor angular speed for the linear parameter varying approach and a conventional design.@en