A dual problem in ℌ2 decentralized control subject to delays

It has been shown that the decentralized ℌ₂ model matching problem subject to delay can be solved by decomposing the controller into a centralized, but delayed, component and a decentralized FIR component, the latter of which can be solved for via a linearly constrained quadratic program. In this paper, we derive the dual to this optimization problem, show that strong duality holds, and exploit this to further analyze properties of the control problem. Namely, we determine a priori upper and lower bounds on the optimal ℌ₂ cost, and obtain further insight into the structure of the optimal FIR component. Furthermore, we show how the optimal dual variables can be used to inform communication graph augmentation, and illustrate this idea with a routing problem.