Abstract
We study the stabilizability of uncertain stochastic 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 extend previous results by deriving sufficient conditions for internal and external stabilizability of multi-state linear and time-invariant plants. In accordance with previous publications, stabilizability of unstable plants is possible 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 studied using a small-gain argument.
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