Networked stabilization with polar logarithmic quantization

This paper studies the use of the polar logarithmic quantization (PLQ) for multi-input systems under state feedback. It is shown that the PLQ induces sector bounded time-varying uncertainties in multiplicative and relative forms for vector-valued analog signals, similar to those in the scalar case. Optimal quantization is obtained through minimization of the quantization errors that are quantified explicitly. Furthermore, feedback stabilization is investigated, and the coarsest quantization density (CQD) is obtained. Results in this paper are illustrated by a numerical example.