Abstract

In this paper we consider the infimal signal-to-noise ratio (SNR)required for stabilisation of a linear time invariant (LTI) scalar unstable plant over a class of additive coloured Gaussian noise channels. We apply recent results in the literature to obtain the feedback capacity of such a class of channels. We prove that the infimal SNR constrained LTI solution, when dealing with a scalar unstable plant, does achieve a channel feedback capacity equal to the infimal rate of transmission required for stability. The optimality of such channel feedback capacity is a non trivial result since we consider additive 1st order moving average (MA) and autoregressive moving average (ARMA) coloured noise.