Stochastic Stabilization of Partially Observed and Multi-Sensor Systems Driven by Gaussian Noise under Fixed-Rate Information Constraints

Abstract: 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.