Stabilisation Over Signal-to-Noise Ratio Constrained Channels: Robust Analysis for the Discrete-Time Case

The presence of a communication channel model in a feedback loop is known to impose a new class of fundamental limitations over its channel signal-to-noise ratio (SNR) when the discrete-time plant model is unstable. These type of fundamental limitations, in the presence of unstable plant poles, are worsened by non-minimum phase zeros (either from the plant or channel model) and plant time delay. In this paper we extend the analysis of such feedback systems by studying the effects of model uncertainties on the infimal SNR required to stabilize the plant. We consider here the additive coloured Gaussian channel (ACGN) model with memory, for which we then obtain the infimal SNR subject to plant, channel and noise model uncertainties. We observe that the infimal channel SNR is increased by these model uncertainties. Furthermore we use the main result to study the effect of channel model time delay.