Abstract: A design method of state feedback controller with sparse structure is proposed via alternating direction method of multipliers（ADMM） for inter-connected systems, which consist of a number of subsystems. Firstly, the relation between the cardinality of feedback gain and the number of feedback channels in the feedback topology is established. The cardinality function, The matrix potential function which represents the feedback gain sparsity is weighted into the objective function of optimal control. Secondly, the ADMM is employed to alternately optimized the sparsity of the feedback gain and the control object function, by which the feedback gain matrix with sparse structure is obtained. Finally, the proposed method is applied to inter-connected power systems, and the effectiveness and merits of the method is validated.