Controlling the flow of information in feedback systems with measurement quantization

Approaches to the analysis and design of feedback control systems in which measurement quantization is present are discussed. The author regards a quantized measurement of a real number simply as a partial observation of that number and not as a straightforward approximation with associated error. As a consequence, the results have an information theoretic component that is absent from earlier research, the majority of which deals with measurement quantization by means of signal-plus-noise models and least-squares theory. It is possible to compute an upper bound on the asymptotic accuracy (measured as a mutual information) with which the current state of a linear system can be specified given a long record of quantized measurements. In deriving this upper bound, it is shown how input to the system can be used as information-gathering tools, and an observer-like construction for systems with quantized outputs is obtained. The results have some interesting system theoretic ramifications, and they form the foundation for a theory of observability for state-space systems with piecewise constant output. This theory differs from the usual one in several significant ways, and the utility of its attendant formalism is demonstrated by some simple examples