# Controllability of Linear Positive Systems: An Alternative Formulation

## TL;DR

This paper introduces a new formulation for controllability in single input linear positive systems, focusing on controllability within specific regions of the positive orthant, with practical verification methods.

## Contribution

It presents an alternative controllability formulation tailored for subsets of the positive orthant, including geometric analysis and verifiable conditions for controllable regions.

## Key findings

- Developed a geometric framework for controllable subsets
- Provided numerically verifiable conditions for polyhedrality
- Offered a method to check controllability of target sets

## Abstract

An alternative formulation for the controllability problem of single input linear positive systems is presented. Driven by many industrial applications, this formulations focuses on the case where the region of interest is only a subset of positive orthant rather than the entire positive orthant. To this end, we discuss the geometry of controllable subsets and develop numerically verifiable conditions for polyhedrality of controllable subsets. Finally, we provide a method to check for controllability of a target set based on our approach.