  The aim of this paper is to prove a Kolmogorov-type result for a
nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time
dependence. The existence of a torus with a prefixed Diophantine frequency is
shown in the forced system, provided that the perturbation is real-analytic and
(exponentially) decaying with time. The advantage consists of the possibility
to choose an arbitrarily small decaying coefficient, consistently with the
perturbation size.
