  This paper studies state quantization schemes for feedback stabilization of
control systems with limited information. The focus is on designing the least
destabilizing quantizer subject to a given information constraint. We explore
several ways of measuring the destabilizing effect of a quantizer on the
closed-loop system, including (but not limited to) the worst-case quantization
error. In each case, we show how quantizer design can be naturally reduced to a
version of the so-called multicenter problem from locational optimization.
Algorithms for solving such problems are discussed. In particular, an iterative
solver is developed for a novel weighted multicenter problem which most
accurately represents the least destabilizing quantizer design.
