On a problem related to application of digital networked communication technology to stabilization of noisy plants over noisy channels

This paper addresses the stabilization problem involving communication errors and capacity constraints. Discrete-time partially observed unstable linear systems perturbed by exogenous uniformly bounded disturbances are studied. Unlike the classic theory, the sensor signals are transmitted to the controller over a noisy digital link. How much the capacity of this link should be in order that the stabilization be possible? We show that the capability of the noisy channel to serve almost sure stability is identical to exactly its capability to communicate information with no error. In other words, the answer to the above question is given by the standard characteristics of the latter capability, i.e., the zero-error capacity of the channel. The zero-error capacity in the presence of a perfect feedback communication link is concerned here. This is true even if there is no such a link in fact. Since the zero-error capacity may be greater with feedback than without, the class of systems almost surely stabilizable via a given channel appears to be wider than expected. To justify this, we show that perfect transmission of as much information as desired can be arranged from the controller to the sensor by means of control actions upon the plant without violating the main objective of keeping the stabilization error a.s. bounded. A particular scheme for such a transmission is offered