Channel signal-to-noise ratio constrained feedback control: performance and robustness

The limitations in performance and robustness imposed by explicitly considering a communication channel in a control loop have received increased attention in recent years. Previous results in the literature have stated these limitations in terms of a minimal transmission data rate necessary for stabilisation. In this paper a signal-to-noise ratio (SNR) approach is used to study two specific cases: (i) performance in terms of model matching and (ii) robustness against a multiplicative uncertainty in the plant model. The analysis performed leads to closed-form expressions that allow the quantification of the extra SNR required in both cases.