Feedback control systems as users of a shared network: Communication sequences that guarantee stability

We investigate the stability of a collection of systems which are governed by linear dynamics and operate un-der limited communication. We view each system and its feedback controller as users on an idealized shared network which grants access only to a few system-controller pairs at any one time. A communication se-quence, which plays the role of a network admission pol-icy, species the amount of time available for each sys-tem to complete its feedback loop. Using Lyapunov the-ory, we give a suÆcient condition for the existence of a stabilizing communication sequence and show how one can be constructed in a way that minimizes network us-age. Our solution depends on the parameters of the un-derlying system(s) and on the number of controller-plant connections that can be maintained simultaneously. We include simulation results illustrating the main ideas.