Performance limitations for SISO LTI plants controlled over SNR constrained channels

This paper presents performance limitations in the control of single-input single-output (SISO) linear time-invariant (LTI) plants over signal-to-noise ratio (SNR) constrained channels. Our main result is a closed form characterization of the minimal stationary plant output variance when the controller has access to plant output measurements and the channel is placed between the controller and the actuator. We explicitly quantify the effects of plant dynamical features, namely unstable poles, non-minimum phase zeros, and frequency response, as well as the effects of channel feedback, on the best achievable performance. Our results shed light into the interplay between optimal performance and SNR constraints.