In this paper we consider practical stabilization strategies of
scalar linear systems by means of quantized feedback maps which
use a minimal number of quantization levels. These stabilization
schemes are based on the chaotic properties of piecewise affine
maps and their performance can be analyzed in terms of the mean
time needed to shrink the system from an initial interval into a
fixed target interval. We show here that this entrance time grows
linearly with respect to the contraction rate defined as the quotient
of the length of the initial and target interval respectively.
Estimations are obtained using denumerable Markov chains arguments.