# Criterion for robustness of global asymptotic stability to perturbations of linear time-varying systems

## TL;DR

This paper introduces a new criterion for assessing the robustness of the global asymptotic stability of linear time-varying systems' zero solution against potentially unbounded disturbances, using logarithmic norms.

## Contribution

It presents a novel stability robustness criterion for LTV systems under unbounded perturbations, utilizing logarithmic norms to connect stability with topological properties.

## Key findings

- Established a criterion for robustness of stability in LTV systems
- Applied logarithmic norm to analyze stability under disturbances
- Provided a topological perspective on stability robustness

## Abstract

In this brief note, we establish a novel criterion for robustness of global asymptotic stability of zero solution of LTV system $\dot x=A(t)x$ in the presence of possibly unbounded perturbations (external disturbances). To prove the result, logarithmic norm will be used under which the stability becomes a topological notion depending on the chosen vector norm in the state-space $\mathbb{R}^n.$