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

Exact Computation of LTI Reach Set from Integrator Reach Set with Bounded Input