H∞ control for discrete-time systems by quantized state feedback

This paper is concerned with the quantized state feedback H-infinity control problem for discrete-time linear time-invariant (LTI) systems. The quantizer considered here is dynamic and composed of an adjustable "zoom" parameter and a static quantizer. Static quantizer ranges are with practical significance and fully considered here. Firstly, by taking quantization errors into account, a quantized control strategy is derived such that the quantized closed-loop system is asymptotically stable and with a prescribed H-infinity performance bound. Then, based on this result, an iterative LMI-based optimization algorithm is proposed to optimize the static quantizer ranges with meeting H-infinity performance requirements for closed-loop systems. An example is presented to illustrate the effectiveness of the proposed method.