Networked control systems for multi-input plants based on polar logarithmic quantization

This paper investigates the use of polar logarithmic quantization (PLQ) for multi-input systems, and the corresponding design issues for the underlying networked control system (NCS). It is shown that the PLQ induces sector bounded nonlinear uncertainties in multiplicative and relative forms for vector-valued analog signals, similar to those in the scalar case. For the two-input NCS, optimal quantization is obtained through minimization of the quantization error that is quantified explicitly. The results are extended to more than two-input NCSs with an upper bound derived for the quantization error. Feedback stabilization and control of the NCS are also investigated under the PLQ at the plant input under state feedback. The coarsest quantization density (CQD) is studied and obtained. Results in this paper are illustrated by a numerical example.