On the Minimal Average Data-Rate that Guarantees a Given Closed Loop Performance Level

This paper deals with control system design subject to average data-rate constraints. By focusing on SISO LTI plants, and a class of source coding schemes, we establish lower and upper bounds on the minimal average data-rate needed to achieve a prescribed performance level. We also guarantee the existence of a specific source coding scheme, within the proposed class, that achieves the desired performance level at average data-rates below our upper bound. Our results are based upon a recently proposed framework to address control problems subject to average data-rate constraints.