This paper deals with the problem of decentralized control synthesis. We seek to find structured controllers that are stably realizable over the underlying network. We address the problem using an operator form of discrete-time linear systems. This allows for uniform treatment of various classes of linear systems, e.g., Linear Time Invariant (LTI), Linear Time Varying (LTV), or linear switched systems. We combine this operator representation for linear systems with the classical Youla parameterization to characterize the set of stably realizable controllers for a given network structure. We show that if the structure satisfies certain subspace like assumptions, then both the stability and performance problems can be formulated as convex optimization and more precisely as tractable model-matching problems. Furthermore, we show that the structured controllers found from our approach can be stably realized over the network.