  We investigate the stabilization of unstable multidimensional partially
observed single-sensor and multi-sensor linear systems driven by unbounded
noise and controlled over discrete noiseless channels under fixed-rate
information constraints. Stability is achieved under fixed-rate communication
requirements that are asymptotically tight in the limit of large sampling
periods. Through the use of similarity transforms, sampling and random-time
drift conditions we obtain a coding and control policy leading to the existence
of a unique invariant distribution and finite second moment for the sampled
state. We use a vector stabilization scheme in which all modes of the linear
system visit a compact set together infinitely often. We prove tight necessary
and sufficient conditions for the general multi-sensor case under an assumption
related to the Jordan form structure of such systems. In the absence of this
assumption, we give sufficient conditions for stabilization.
