- This work is a continuation of recent efforts aimed at understanding the interplay of control, communication and computation in systems whose sensors, actuators and computing elements are distributed across a network. We investigate the simultaneous stabilization of a group of linear systems whose feedback loops are closed over an idealized shared medium. The capacity of that medium is constrained so that only a limited number of controller-plant connections can be accommodated at any one time. We introduce a feedback communication policy - inspired by previous work on queuing systems and real-time scheduling - for deciding which system(s) should be admitted into the network and for how long. The use of feedback in making communication decisions results in a set of autonomous dynamical systems which are coupled to one another due to the presence of communications constraints. We give conditions for the stability of the collection under the proposed communication policy and present simulation results that illustrate our ideas.