Explicit conditions for stabilization over noisy channels subject to SNR constraints

In this paper, we analyze the stability of networked control systems when parallel additive white noise (AWN) channels are considered. We assume that the parallel AWN channels are individually constrained in its signal to noise ratio (SNR). We obtain explicit conditions on the minimum requirements on the channel SNRs necessary for stability for a set of particular plant structures. Our results show explicitly the role played by the unstable plant pole directions in the stability of NCSs. We also show that, when state feedback control is used, a simple characterization on the channel SNRs for stability can be given.