Robust signal-to-noise ratio constrained feedback control

The explicit consideration of a communication channel model in a feedback control loop is known to create a new type of fundamental limitation for stabilisability on the channel signal-to-noise ratio (SNR) when the continuous-time plant model is unstable. In this paper we quantify these type of limitations subject to model uncertainties when a robust controller is in place instead of the optimal SNR controller. We consider here the additive coloured Gaussian channel with bandwidth limitation model, for which we then quantify the infimal SNR subject to the simultaneous presence of plant, channel and noise model uncertainties. We observe that the infimal SNR expression is modified by the presence of model uncertainties and by the mismatch between the robust controller solution and the optimal controller solution achieving the infimal SNR limitation.