Performance limitations for SISO LTI plants controlled over SNR constrained channels

Abstract

This paper presents performance limitations in the control of single-input single-output (SISO) linear timeinvariant (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.

Performance limits in the control of single‐input linear time‐invariant plants over fading channels

“…However, the benefits of channel feedback on closed loop performance have not been explicitly characterised. The case of SNR constrained channels and SISO plant models has been addressed by us in the preliminary publication [28]. Related results are presented in [29], where SNR‐constrained architectures for single‐input–multiple‐output (SIMO) plants with channel feedback are studied.…”