In order to enhance the performance of cyberphysical systems, this paper proposes the integrated design of distributed controllers for distributed plants and the control of the communication network. Conventional design methods use static interfaces between both entities and therefore rely on worst-case estimations of communication delay, often leading to conservative behavior of the overall system. By contrast, the present approach establishes a robust distributed model-predictive control scheme, in which the local subsystem controllers operate under the assumption of a variable communication schedule that is predicted by a network controller. Using appropriate models for the communication network, the network controller applies a predictive network policy for scheduling the communication among the subsystem controllers across the network. Given the resulting timevarying predictions of the age of information, the paper shows under which conditions the subsystem controllers can robustly stabilize the distributed system. To illustrate the approach, the paper also reports on the application to a vehicle platooning scenario.