On design of finite-level quantization feedback control

This paper studies quantized feedback control of discrete-time linear systems using a finite-level quantizer. Motivated by the fact that most feedback communication channels allow a moderate bit rate, we are not particularly concerned with the problem of finding the minimum bit rate of feedback for a given control objective. Instead, we assume that a moderate bit rate is available. We introduce a dynamic scaling method and combine it with a known logarithmic quantization method. Using this approach, satisfactory control of linear systems can be achieved using a quantizer with a moderate number of quantization levels. Two main advantages of this approach are 1) it is very easy to implement, and 2) the closed-loop system behaves as if there was no limitation on the number of quantization levels when the state of the system is within a “normal” operating range. These features are important for practical applications of quantized feedback control.