  We study a stabilization problem of linear uncertain systems with parametric
uncertainties via feedback control over data-rate-constrained channels. The
objective is to find the limitation on the amount of information that must be
conveyed through the channels for achieving stabilization and in particular how
the plant uncertainties affect it. We derive a necessary condition and a
sufficient condition for stabilizing the closed-loop system. These conditions
provide limitations in the form of bounds on data rate and magnitude of
uncertainty on plant parameters. The bounds are characterized by the product of
the poles of the nominal plant and are less conservative than those known in
the literature. In the course of deriving these results, a new class of
nonuniform quantizers is found to be effective in reducing the required data
rate. For scalar plants, these quantizers are shown to minimize the required
data rate, and the obtained conditions become tight.
