# Stability and stabilization of linear positive systems on time scales

## TL;DR

This paper establishes a criterion for the exponential stability of positive linear systems on time scales based on polynomial coefficients and derives conditions for their positive stabilizability, unifying continuous and discrete cases.

## Contribution

It provides a new stability criterion for positive systems on time scales and characterizes positive stabilizability with necessary and sufficient conditions.

## Key findings

- Positive linear systems are exponentially stable iff polynomial coefficients are positive.
- Derived necessary and sufficient conditions for positive stabilizability.
- Unified stability analysis applicable to continuous and discrete systems.

## Abstract

It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then this fact is used to find necessary and sufficient conditions of positive stabilizability of a positive control system on a time scale.