Control over direct and feedback path signal-to-noise ratio constrained channels

In this paper we address the problem of signal-to-noise ratio (SNR) constrained channels simultaneously located over the direct path (between the controller and the plant) and the feedback path (between the plant and the controller) within a feedback control configuration. We first study the presence of memoryless additive white Gaussian noise (AWGN) channels. For this channel model we consider the suboptimal approaches that give priority to one channel over the other, and then compare them with the approach that simultaneously minimize the SNR of both channels. We also discuss the case in which the additive noise process is the same for both channels. We then extend the results to the additive colored Gaussian noise (AGCN) channel model.