We study the problem of mapping discrete-time linear controllers into potentially higher order linear controllers with predefined structural constraints. Our work has been motivated by the Wireless Control Network (WCN) architecture, where the network itself behaves as a distributed, structured dynamical compensator. We make connections to model reduction theory to derive a method for the controller embedding based on minimization of the H∞-norm of the error system. This allows us to frame the problem as synthesis of optimal structured linear controllers, which enables the utilization of design-time iterative procedures for systems’ approximation. Finally, we illustrate the use of the mapping procedure by embedding PID controllers into the WCN substrate, and show how to reduce the computation overhead of the approximation procedure.