Bounds on the optimal quantization performance of dynamically quantized linear systems with bounded noise

Abstract

This paper studies a class of quantized linear control systems with diagonalizable system matrices and perturbed by bounded noise. The quantization performance of such systems is measured with the supremum of the quantization error sequence. Our goal is to improve this performance (reduce the quantization error) through designing appropriate quantization policies. Due to their efficiency, the dynamic quantization policies are considered in this paper. A lower bound on the optimal (minimum) quantization error is provided. We also propose a new quantization policy, whose quantization error is an upper bound on the optimal one. A more tractable upper quantization error bound is derived from the new policy. It is shown through simulations that the new policy's quantization error is very close to the lower bound, which confirms both the tightness of the lower bound and the efficiency of the new policy. The achieved lower and upper quantization error bounds, together with the quantization error of the new quantization policy, may provide a good indication on the optimal quantization performance. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society.