An often cited motivation for using decomposition-based optimization methods to solve engineering system design problems is the ability to apply discipline-specific optimization techniques. For example, structural optimization methods have been employed within a more general system design optimization framework. We propose an extension of this principle to a new domain: control design. The simultaneous design of a physical system and its controller is addressed here using a decomposition-based approach. An optimization subproblem is defined for both the physical system (i.e., plant) design and the control system design. The plant subproblem is solved using a general optimization algorithm, while the controls subproblem is solved using a new approach based on optimal control theory. The optimal control solution, which is derived using the the Minimum Principle of Pontryagin (PMP), accounts for coupling between plant and controller design by managing additional variables and penalty terms required for system coordination. Augmented Lagrangian Coordination is used to solve the system design problem, and is demonstrated using a circuit design problem.