Almost Sure Nonobservability and Unstabilizability of Unstable Noisy Linear Plants via Communication Channels with Packet Losses

We show that unstable linear plants affected by uniformly bounded and arbitrarily small disturbances cannot be stabilized or observed with a nonzero probability over communication channels with data dropout. Specifically, both estimation and stabilization errors are almost surely unbounded. This is true for all non-anticipating algorithms of estimation and stabilization with infinite memories, provided that the channel meets some natural requirements. They are satisfied e.g., if packet losses happen with a given nonzero probability and independently of each other and the system noise.