Optimal quantization interval design of dynamic quantizers which satisfy the communication rate constraints

This paper proposes the design method of the dynamic quantizer for the networked control systems. It is well known that the dynamic quantizers, which consist of filter and static quantizer, are effective for compressing the data with small quantization error of control. Many methods for designing the dynamic quantizers have been proposed from the perspective of filter design. When it is required to control with network communication, the data size of signal should be minified appropriately by quantizers because of the communication rate constraint. Since the quantization interval (distance between two quantizer outputs) of the quantizer makes an impact on the data rate, determination of quantization interval is important matter in the dynamic quantizers. However, the design method of quantization interval has not been proposed explicitly in the past researches of the dynamic quantizer design. In this paper, we propose the design method of the smaller quantization interval which satisfy the communication rate constraints. The design method is derived as an LMI problem based on the invariant set analysis. By the proposed method, the quantization interval guarantees that the signals are quantized appropriately within the given data size. The effectiveness is illustrated by numerical examples.