On the stability of systems of two linear first-order ordinary differential equations

TL;DR

This paper develops new stability criteria for systems of two linear first-order ODEs using the Riccati equation method, linking some criteria to the classical Routh-Hurwitz criterion.

Contribution

Introduces novel stability criteria for 2D linear ODE systems based on Riccati equations, connecting them to established Routh-Hurwitz conditions.

Findings

Two new stability criteria derived for 2D linear systems.

Certain criteria imply the classical Routh-Hurwitz criterion.

Enhances understanding of stability analysis methods.

Abstract

The Riccati equation method is used to establish some new stability criteria for systems of two linear first-order ordinary differential equations. It is shown that two of these criteria in the two dimensional case imply the Routh - Hurwitz's criterion.