  We provide a solution to the heretofore open problem of stabilization of
systems with arbitrarily long delays at the input and output of a nonlinear
system using output feedback only. The solution is global, employs the
predictor approach over the period that combines the input and output delays,
addresses nonlinear systems with sampled measurements and with control applied
using a zero-order hold, and requires that the sampling/holding periods be
sufficiently short, though not necessarily constant. Our approach considers a
class of globally Lipschitz strict-feedback systems with disturbances and
employs an appropriately constructed successive approximation of the predictor
map, a high-gain sampled-data observer, and a linear stabilizing feedback for
the delay-free system. The obtained results guarantee robustness to
perturbations of the sampling schedule and different sampling and holding
periods are considered. The approach is specialized to linear systems, where
the predictor is available explicitly.
