Abstract
This paper is concerned with the quantized state feedback H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> control problem for discrete-time linear timeinvariant (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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> performance bound. Then, based on this result, an iterative LMI-based optimization algorithm is proposed to optimize the static quantizer ranges with meeting H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> performance requirements for closed-loop systems. An example is presented to illustrate the effectiveness of the proposed method.
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