Output feedback stabilisation over bandwidth limited, signal to noise ratio constrained communication channels

Stabilisability of an open loop unstable plant is studied under the presence of a bandwidth limited additive coloured noise communication channel with constrained Signal to Noise Ratio. The problem is addressed through the use of an LTI filter explicitly modelling the bandwidth limitation, and another LTI filter to model the additive coloured noise. Results in this paper show that a bandwidth limitation increases the minimum value of Signal to Noise Ratio required for stabilisability, in comparison to the infinite bandwidth, white noise case. Examples are used to illustrate the results in the continuous and discrete framework.