Attainability of the minimum data rate for stabilization of linear systems via logarithmic quantization

This paper investigates the attainability of the minimum average data rate for stabilization of linear systems via logarithmic quantization. It is shown that a finite-level logarithmic quantizer suffices to approach the well-known minimum average data rate for stabilizing an unstable linear discrete-time system under two basic network configurations. In particular, we derive explicit finite-level logarithmic quantizers and the corresponding controllers to approach the minimum average data rate.