Aggregate control of clustered networks with inter-cluster time delays

We address a control problem for networks that have multiple dense clusters with sparse interconnection structure. By making use of the time-scale separation properties of such networks, we design state-feedback controllers at the cluster level to guarantee stability in the presence of time varying delays in the inter-cluster feedback channels. Applying results from singular perturbation theory, we show that when these individual controllers are implemented on the actual network model, the closed-loop response is close to that obtained from the approximate models, provided that the clustering is strong and the time delay is below the maximum limit. The design procedure is demonstrated by a simulation example.