An Achievable Data-Rate Region Subject to a Stationary Performance Constraint for LTI Plants

This note studies the performance of control systems subject to average data-rate limits. We focus on a situation where a noisy LTI system has been designed assuming transparent feedback and, due to implementation constraints, a source coding scheme (with unity signal transfer function) has to be deployed in the feedback path. For this situation and by focusing on a specific source coding scheme, we give a closed-form upper bound on the minimal average data-rate that allows one to attain a given performance level. Instrumental to our main result is the explicit solution of a related signal-to-noise ratio minimization problem, subject to a closed loop performance constraint.