# A linear programming approach to approximating the infinite time reachable set of strictly stable linear control systems

## TL;DR

This paper introduces a novel linear programming method to approximate the infinite time reachable set of stable linear control systems, avoiding traditional forward iteration techniques.

## Contribution

It presents a new numerical approach that computes outer approximations of the limit set using linear programming with system dynamics constraints.

## Key findings

- Efficient computation of outer approximations of the infinite reachable set.
- Avoids the need for iterative forward simulation of finite-time reachable sets.
- Provides a polytope approximation with fixed facet normals.

## Abstract

We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with fixed facet normals as an outer approximation of the limit set. In particular, this approach does not rely on forward iteration of finite-time reachable sets.