This paper proposes a design method for a robust controller to improve the stability and system dynamic behavior for variable speed wind energy conversion systems. By analyzing the mathematical model of a wind power conversion system, control strategies for both a generator-side converter and a grid-side converter are given. For the generator-side converter, the well-known maximum power point tracking method is employed, while for the grid-side converter, a robust controller is presented based on passivity theory. The $L_{2}$-gain performance is analyzed using linear matrix inequality. Moreover, in order to accelerate the dynamic response and reduce the DC link voltage fluctuations, the optimum equilibrium points of the system are designed based on the analysis of the dynamic equations of the DC link voltage. Finally, the proposed method is verified a by hardware-in-the-loop simulation.