This paper presents synthesis results for distributed controllers for interconnected linear time-invariant systems. The setting of the paper is in discrete time. Based on the theory of dissipative dynamical systems, analytical conditions for robust stability and robust H? performance of networks of interconnected systems are derived in terms of feasibility tests of linear matrix inequalities. From these conditions, computationally tractable synthesis conditions are derived and an iterative D-K type of synthesis algorithm is proposed that yields a robust distributed controller. Convergence properties of the algorithm are inferred. In addition, based on necessary and sufficient conditions for stability using static state feedback, computationally tractable synthesis procedures are derived that yield a distributed controller with an interconnection structure that can be chosen arbitrary. An algorithm is presented that uses these synthesis procedures to find a controller with a distributed structure. The synthesis results from both approaches involve convex optimization problems in the form of linear matrix inequalities (LMIs) which are solved in a centralized way. A complexity analysis for the synthesis results is incorporated. The synthesis algorithms are illustrated on examples of electrical power systems and a system with delays in the interconnections.