In this paper, H_∞ state feedback control for weakly coupled systems is investigated. The attention is focused on the design of the high-order approximate H_∞ controller which is based on the numerical solutions. A novel contribution is that a new iterative algorithm is derived by combining Newton's method and the fixed point algorithm. As a result, H_∞ controller can be constructed in the same dimension of the subsystems. It is newly proved that the proposed algorithm has the quadratic convergence. Moreover, it is shown that the resulting controller achieves O(ε^2κ) approximation of the optimal H_∞ cost. As another important feature, if the coupling parameter is unknown, it is also shown that the parameter independent decentralized controllers achieve O(ε) approximation.