# On stability of linear neutral differential equations with variable delays

## TL;DR

This paper reviews existing stability tests and introduces new explicit exponential stability conditions for linear scalar neutral differential equations with variable delays, including generalizations with multiple delays and distributed delays.

## Contribution

It provides a comprehensive review and new explicit stability criteria for neutral differential equations with variable delays and their generalizations.

## Key findings

- New explicit exponential stability conditions derived.
- Extended stability analysis to equations with multiple and distributed delays.
- Comparison with existing stability tests included.

## Abstract

We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays $$ \dot{x}(t)-a(t)\dot{x}(g(t))+b(t)x(h(t))=0, $$ where $$ |a(t)|<1,~ b(t)\geq 0, ~h(t)\leq t, ~g(t)\leq t, $$ and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.