Stability criterion for linear systems of ordinary differential equations

TL;DR

This paper introduces a new stability criterion for linear ODE systems using the Riccati equation method, comparing it with existing methods through examples.

Contribution

It presents a novel stability criterion based on Riccati equations, expanding the analytical tools for linear system stability analysis.

Findings

The new criterion is effective in stability analysis.

Comparison shows advantages over Lyapunov and Bogdanov methods.

The criterion performs well with Lozinskii logarithmic norms and freezing method.

Abstract

The Riccati equation method is used to establish a new stability criteria for linear systems of ordinary differential equations. Two examples are presented in which the obtained result is compared with the results obtained by the Lyapunov and Bogdanov methods, by a method involving estimates of solutions in the Lozinskii logarithmic norms and by the freezing method.