Signal-to-Noise Ratio Limitations in Feedback Control

Abstract

The present article is focused in the area of control over networks. The main difference with classic control is that we deal with an explicit communication channel model in the feedback control structure. The channel model is modeled as to have limited bandwidth and additive colored Gaussian noise. This allows us to study the interaction between the control and communication goals. We first briefly revisit the assumption behind the present work and formally define the problem at hand. We then review its solution in the form of the Signal-to-Noise Ratio (SNR) fundamental limitation for stabilizability result. We extend the stabilizability result to include the following performance scenarios: closed-loop arbitrary pole assignment, robustness, set point tracking and the effect of channel input quantization. We finally conclude the present paper by studying the capacity resulting from these performance limitations for the case of a memoryless additive white Gaussian noise (AWGN) channel.