Quantized Dynamic Output Feedback H∞ Control for Discrete-time Systems with Quantizer Ranges Consideration

The problem of quantized dynamic output feedback H∞ control for discrete-time linear time-invariant (LTI) systems is investigated in this paper. The quantizer considered is dynamic and composed of an adjustable “zoom” parameter and a static quantizer. Static quantizer ranges are of practical significance and are fully considered. First, taking quantization errors into account, a quantized control strategy is dependent not only on the controller states but also on the system measurement outputs, which is proposed such that the quantized closed-loop system is asymptotically stable and with a prescribed H∞ performance bound. Then, on the basis of this result, an iterative LMI-based optimization algorithm is developed to optimize the static quantizer ranges to meet H∞ performance requirements for closed-loop systems. An example is presented to illustrate the effectiveness of the proposed method.