Short-Period Communication and the Role of Zero-Order Holding in Networked Control Systems

We discuss controller design for a networked control system (NCS) in which a stochastic linear time invariant (LTI) plant communicates with a controller over a shared medium. The medium supports a limited number of simultaneous connections between the controller and the plant's sensors and actuators, possibly subject to transmission delays. We restrict communication to periodic medium access sequences which preserve the structural properties of the plant, thus decoupling the selection of the communication from that of the controller. Using the plant's controllability/observability indices as a guide for allocating access, we show that the period of the sequences in question can be shorter than previously established. In addition, we explore the use of sequences designed for a simple NCS model, in which sensors and actuators are "ignored" by the controller when they are not actively communicating, in a more complex, but practical, setting that includes zero-order holding. We include a numerical experiment that illustrates our results in the context of LQG control.