The stabilization of period doubling bifurcations for discrete-time no
nlinear systems is investigated. It is shown that generically such bif
urcations can be stabilized using smooth feedback, even if the lineari
zed system is uncontrollable at criticality. In the course of the anal
ysis, expressions are derived for bifurcation stability coefficients o
f general n-dimensional systems undergoing period doubling bifurcation
. A connection is determined between control of the amplitude of a per
iod doubled orbit and the elimination of a period doubling cascade to
chaos. For illustration, the results are applied to the Henon attracto
r.