# On stability of linear neutral differential equations in the Hale form

## TL;DR

This paper derives explicit exponential stability conditions for linear scalar neutral differential equations with variable coefficients and delays, including cases with bounded and unbounded delays, advancing the understanding of their stability behavior.

## Contribution

It provides new explicit stability criteria for neutral equations with variable delays, covering both bounded and unbounded delay scenarios.

## Key findings

- Explicit exponential stability conditions for bounded delays.
- An asymptotic stability condition for unbounded delays.
- Enhanced understanding of stability in neutral differential equations.

## Abstract

We present new explicit exponential stability conditions for the linear scalar neutral equation with two variable coefficients and delays $$ (x(t)-a(t)x(g(t)))'=-b(t)x(h(t)), $$ where $|a(t)|<1$, $b(t)\geq 0$, $h(t)\leq t$, $g(t)\leq t$, in the case when the delays $t-h(t)$, $t-g(t)$ are bounded, as well as an asymptotic stability condition, if the delays can be unbounded.