Stochastic Stabilization of Partially Observed and Multi-Sensor Systems   Driven by Gaussian Noise under Fixed-Rate Information Constraints
  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. 
Andrew P. Johnston and Serdar Y\"uksel
math.OC cs.IT math.IT