Information theoretic study of the signaling problem in decentralized stabilization of noisy linear systems

We study the problem of distributed stabilization of linear systems over communication channels. Building on our earlier work, we adopt an information theoretic look at the signaling problem when the system and observations are noisy. We provide a lower bound on the average sum-rate, which is tight when the system noise is absent. We further show that when the system and observations are noisy, the signaling process involves coding over an unknown channel with unequal side information between the stations, and as such its construction is fairly complicated. This leads to new insights on designing distributed controllers connected over channels.