We consider the problem of constructing decentralized state feedback controllers for linear continuous-time systems. Different from existing approaches, where the topology of the controller is fixed a priori, the topology of the controller is part of the optimization problem. Structure optimization is done in terms of a minimization of the required feedback links and subject to a predefined bound on the tolerable loss of the achieved H-infinity-performance of the decentralized controller compared to an H-infinity-optimal centralized controller. We develop a computationally efficient formulation of the decentralized control problem by convex relaxations which makes it attractive for practical applications. The proposed design algorithm is applied to design sparse wide area control of a 3-area, 6-machine power system. (C) 2013 Elsevier Ltd. All rights reserved.