Stabilising decentralised linear systems under data rate constraints

This paper considers the following question: given a deterministic linear plant with multiple sensors and controllers, how can one characterise the combination of channel data rates between all sensor-controller pairs which permits stability to be achieved? Under different stability objectives, two sets of data rate inequalities which must be satisfied by any stabilising decentralised coding and control scheme are presented. It is then shown that if another set of inequalities is feasible then a stabilising decentralised coding and control scheme can always be constructed. Finally, a tight data rate inequality for stabilisability is obtained for a special class of decentralised plant.