  An analytical prediction is established of how an isolated many-body quantum
system relaxes towards its thermal long-time limit under the action of a
time-independent perturbation, but still remaining sufficiently close to a
reference case whose temporal relaxation is known. This is achieved within the
conceptual framework of a typicality approach by showing and exploiting that
the time-dependent expectation values behave very similarly for most members of
a suitably chosen ensemble of perturbations. The predictions are validated by
comparison with various numerical and experimental results from the literature.
