In the present paper we study the fundamental limitations on stability that arise when an additive coloured Gaussian noise (ACGN) channel is explicitly considered in a linear time invariant (LTI) control feedback loop. By considering a linear setting we can express the fundamental limitation on stability as a lower bound in closed-form on the ACGN channel signal-to-noise ratio (SNR). Outside the context of networked control, the obtained lower bound can be interpreted as an H-2 performance limitation. (C) 2010 Elsevier Ltd. All rights reserved.