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Exact Computation of LTI Reach Set from Integrator Reach Set with Bounded Input (2309.08222v3)
Published 15 Sep 2023 in math.OC, cs.SY, eess.SY, and math.DS
Abstract: 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.