Feedback stabilization of uncertain systems using a stochastic digital link

We study the stabilizability of uncertain systems in the presence of finite capacity feedback. Motivated by the structure of communication networks, we consider a stochastic digital link that sends words whose size is governed by a random process. Such link is used to transmit state measurements between the plant and the controller. We derive necessary and sufficient conditions for the internal and the external stabilizability of the feedback loop. In accordance with previous publications, stabilizability of unstable plants is possible if and only if the link's average transmission rate is above a positive critical value. In our formulation the plant and the link can be stochastic. In addition, stability in the presence of uncertainty in the plant is analyzed using a small-gain argument. We show that the critical average transmission rate, for stabilizability, depends on the description of uncertainty and the statistical properties of the plant as well as the link.