 
Summary: Convergence Rate of Quantization Error in Networked Control Systems
Hui Fang and Panos J. Antsakls
Abstract
In this paper, we investigate the problem of convergence
rate of the quantization error in networked control systems.
Given bit rate R, we derive the best convergence rate of the
quantization error together with a corresponding rate al
location strategy. Specifically, using a minmax eigenvalue
problem (MMEP) formulation, it is shown that the error
convergence rate is determined by the ratio between detA
and R where A is the state matrix. It is also shown that the
bit rate R can be optimized through a dynamic quantization
policy among the unstable modes of the system, such that
the convergence rate of the quantization error approaches
the optimal solution to the MMEP problem.
1. Introduction
There is strong ongoing interest in the problem of con
trol under communication constraints; attempting to bring
together classical control theory and practical communi
cation theoretical issues in the design of control system.
