This paper discusses the stabilization of a networked control system (NCS) whose sensors and actuators exchange information with a remote controller over a shared communication medium. Access to that medium is governed by a pair of periodic communication sequences. Under the model utilized here, the controller and plant handle communication disruptions by ``ignoring' (in a sense to be made precise) sensors and actuators that are not actively communicating. It is shown that under mild conditions, there exist periodic communication sequences that preserve the reachability and observability of the plant, leading to a straightforward design of a stabilizing feedback controller.