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.
- Control over the internet
- Fading channels
- Mean square stability robustness
- Quality of Service