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 under 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 sequence, which plays the role of a network admission policy, specifies the amount of time available for each system to complete its feedback loop. Using Lyapunov theory, we give a sufficient condition for the existence of a stabilizing communication sequence and show how one can be constructed in a way that minimizes network usage. Our solution depends on the parameters of the underlying system(s) and on the number of controller-plant connections that can be maintained simultaneously. We include simulation results illustrating the main ideas.