Signal-to-noise ratio constrained feedback control: Robust stability analysis

The explicit consideration of a communication channel model in a feedback control loop is known to be constrained by a fundamental limitation for stabilizability on the channel signal-to-noise ratio (SNR) when the linear time invariant (LTI) plant model is unstable. The LTI modelling approach for real, usually nonlinear, processes compromises accuracy versus complexity of the resulting model. This in turn introduces a gap between the proposed model and the real process, which is known as the model uncertainty. In this paper we then study SNR limitations by considering the continuous-time scenario and the case of an additive coloured Gaussian noise (ACGN) channel with bandwidth limitation, for which we then quantify the infimal SNR subject to the simultaneous presence of plant, channel and noise model uncertainties. We observe, for the special case of memoryless additive white Gaussian noise (AWGN) channels, that the obtained SNR limitation subject to plant model uncertainty can be redefined as a channel capacity limitation for stabilization.