Wind Energy Conversion System (WECS) using a Doubly Fed Induction Generator (DFIG) is popular due to its control flexibility and higher conversion efficiency, but maintaining the operational stability and optimal efficiency under dynamic wind conditions is still a control challenge. In this paper, a nonlinear mathematical model for a DFIG based WECS was developed from fundamentals and its characteristics near the operating point were studied. A Proportional Integral (PI) controller and a Linear Quadratic Regulator (LQR) controller were designed to control the system and the behavior of the closed-loop system with these controllers was studied. While the designed PI controller failed to ensure stability, the LQR controller was giving stability but an LQR controller is vulnerable to loss of stability under uncertainties due to parameter variations or changes in operating points. A suboptimal H∞ controller was then synthesized to obtain robust control. The closed-loop system performance of the DFIG system with the proposed controller was found to be stable and superior to PI and LQR controllers in terms of performance. © 2021, The Korean Institute of Electrical Engineers.