A two-station decentralized LQG problem with noisy communication

We consider a two-station decentralized linear quadratic Gaussian problem, where the stations are allowed to communicate some pieces of information. We investigate a possible sub-optimal approach where the controls are obtained based on two separate centralized problems. Various cases are considered in which the two stations communicate their measurements, their controls or estimates, and their estimation residual through noisy channels. We mainly focus on the closed-loop stability properties. We show that even if the stations communicate all their measurements through low noise or even noiseless channels, the controls obtained from the two centralized LQG problems may fail to stabilize the closed-loop decentralized system