  We consider the injection of a controlled charge from a normal metal into an
edge state of the fractional quantum Hall effect, with a time-dependent voltage
$V(t)$. Using perturbative calculations in the tunneling limit, and a chiral
Luttinger liquid model for the edge state, we show that the electronic
correlations prevent the charge fluctuations to be divergent for a generic
voltage pulse $V(t)$. This is in strong contrast with the case of charge
injection in a normal metal, where this divergence is present. We show that
explicit formul{ae} for the mean injected charge and its fluctuations can be
obtained using an adiabatic approximation, and that non perturbative results
can be obtained for injection in an edge state of the FQHE with filling factor
$ nu=1/3$. Generalization to other correlated systems which can be described
with the Luttinger liquid model, like metallic Carbon nanotube, is given.
