# Asymptotic stability and stability switching for a system of delay differential equations

## TL;DR

This paper investigates the asymptotic stability of a linear delay differential system, providing detailed analysis of the characteristic equation to establish conditions for stability and stability switching.

## Contribution

It offers the first comprehensive necessary and sufficient conditions for stability and stability switching in such delay differential systems.

## Key findings

- Derived necessary and sufficient stability conditions
- Analyzed the characteristic equation in detail
- Described the stability switching phenomena

## Abstract

In this paper, we consider the asymptotic stability for a system of linear delay differential equations. By analysing of the characteristic equation in detail, we have established the necessary and sufficient condition for the asymptotic stability for the zero solution of the system including the stability switching which describe the transition between stability and instability.