  We present a semi-analytical method for exact computation of the boundary of
the reach set of a single-input controllable linear time invariant (LTI) system
with given bounds on its input range. In doing so, we deduce a parametric
formula for the boundary of the reach set of an integrator linear system with
time-varying bounded input. This formula generalizes recent results on the
geometry of an integrator reach set with time-invariant bounded input. We show
that the same ideas allow for computing the volume of the LTI reach set.
