An analogue of Shannon information theory for networked control systems. Stabilization via a noisy discrete channel

The paper addresses feedback stabilization problems in a remote control setup, where the measurements are communicated to the controller over a noisy digital channel. A discrete-time partially observed time-invariant linear systems are studied. It is shown that the classic Shannon´s noisy channel capacity constitutes the border separating the cases where the plant can and, respectively, cannot be feedback stabilized almost surely. A quantized feedback control law stabilizing the system almost surely is proposed.