The problem of static precompensator design for uncertain system to reduce the coupling is considered in this paper. Diagonal dominant is redefined using the $H_2$ norm of the system. Based on this definition, the necessary and sufficient conditions for system diagonal dominant, which are described by Linear Matrix Inequalities (LMIs), are derived. These conditions are extended to design static precompensator for both nominal system and uncertain system. The conditions are in the form of Bilinear Matrix Inequalities (BMIs), and the combined bisection and path-following algorithm is developed to solve the BMIs. An example is given to show the effectiveness of the proposed method.