Feedback Stabilization in the Presence of Fading Channels

In this paper we analyze two classes of analog fading channels placed at the input of the plant. Based on previous results, finding a linear controller that provides Mean Square stability of the closed loop through the channel is equivalent to a robust control synthesis problem, where the nominal generalized plant is deterministic, and the stochastic variables in the channel model are represented as model uncertainty. We show that a FIR AWGN channel with Gaussian coefficients leads to a rank-one (convex) problem, which can be easily solved to find the largest variance of the channel coefficients tolerable by an LTI controller. For a channel which allows for with delays and erasure, we compute the channel probabilities for which Mean Square stability can be provided by an LTI controller.