Basic Idea of Periodically Time-Varying Dynamic Quantizer in Networked Control Systems

Feedback-type dynamic quantizers such as delta-sigma modulators are well known as an effective signal processing method for encoding higher-resolution data into lower-resolution data. Dynamic quantizers are composed of a filter and a static quantizer. In the previous studies, the filter component in the dynamic quantizers were characterized as a time-invariant state equation form. This paper provides a dynamic quantizer form, including periodically time-varying matrices, for improving the control performance under communication rate constraints. The analysis method for periodically time-varying dynamic (PTVD) quantizer is reduced to that for dynamic quantizers using a time-invariant state equation form using the well-known lifting technique. It is expected that the control performance by the proposed PTVD quantizer is better than the dynamic quantizers with the time-invariant filter component. The effectiveness of the designed PTVD quantizer is assessed via numerical examples.