Optimal distributed controllers realizable over any arbitrary delay Networks

We study the notion of network realizability which is the property of a system to be expressed as sub-systems interacting over a given network. In this paper, we consider the problem of finding an optimal network-realizable controller that can stabilize a networked plant while minimizing the H ₂ norm of the closed-loop transfer function under the constraint that both plant and controller are linear networked systems interacting over a given directed delay network. We extend the notion of network realizability from [1], [2] to systems over a broader class of delay networks and analyze the structure of network realizable systems. Using these structural properties, we characterize the set of all stabilizing controllers that are realizable over the given delay network using the Youla parametrization. The H₂ control problem is then cast as a convex optimization problem and its solution is shown to provide the optimal distributed controller over the given delay network. The results of this paper allow one to model, analyze and design systems over arbitrary directed delay networks.