This paper addresses feedback stabilization problems for linear time-invari
ant control systems with saturating quantized measurements. We propose a ne
w control design methodology, which relies on the possibility of changing t
he sensitivity of the quantizer while the system evolves. The equation that
describes the evolution of the sensitivity with time (discrete rather than
continuous in most cases) is interconnected with the given system (either
continuous or discrete), resulting in a hybrid system. When applied to syst
ems that are stabilizable by linear time-invariant feedback, this approach
yields global asymptotic stability.