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

TL;DR

This paper introduces a semi-analytical method for exactly computing the boundary of the reach set of single-input LTI systems with bounded inputs, generalizing previous integrator results and enabling volume computation.

Contribution

It provides a parametric formula for the integrator reach set boundary with time-varying input, extending recent geometric results and allowing volume calculation of LTI reach sets.

Findings

Derived a parametric formula for integrator reach set boundary with time-varying input

Extended geometric analysis to general LTI systems with bounded input

Enabled exact volume computation of LTI reach sets

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.