Analysis and Design of Logarithmic-type Dynamic Quantizer

Abstract

This paper is concerned with quantized feedback control in the case where logarithmic-type dynamic quantizers are adopted instead of conventional static (memoryless) ones. First, when the plant and the state feedback controller are given, the admissible coarsest quantization density which guarantees quadratic stability of the closed loop system is given in a closed form, which does not depend on the choice of controller in contrast to the static quantizer case. Second, when the plant, the state feedback controller and the coarseness of the quantization density are given, we provide a design method of the dynamic quantizers via convex optimization. Third, these results are extended to the case of output feedback control systems. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed method.