A novel approach to the Routh-Hurwitz criterion

Zahreddine, Ziad

doi:10.47974/JIM-2196

Open Access Research Article

A novel approach to the Routh-Hurwitz criterion

^*Ziad ZahreddineCorresponding authorz.zahreddine@kcst.edu.kwDepartment of Mathematics College of Engineering Kuwait College of Science and TechnologyDoha Area, 7th Ring Road, KuwaitView full profile →

* Corresponding author · click or hover a name for details

pp. 2623–2630Vol. 28Issue 7October 2025DOI: 10.47974/JIM-2196XML

Received:: 03 Sep 2024
Published Online:: 07 Oct 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2196
Pages:: 2623–2630

Abstract

The Routh-Hurwitz Criterion is closely related to the stability of a continuous-time system of differential equations. Its main concern is the determination of the number of zeros of the characteristic polynomial of the system with positive or negative real parts and the number of imaginary zeros. We propose a new algorithm to achieve this goal. The new technique is extremely simple to apply since it only requires elementary row operations of an associated determinant. The asymptotic stability of the system falls out as a special case of the newly proposed algorithm. Several randomly chosen examples are given to illustrate the simplicity and the effectiveness of the novel approach.

Keywords

Routh-Hurwitz criterion Stability analysis Continuous-time systems of differential equations Distribution of roots

Subject Classifications

Primary 37C7593C15. Secondary 93D30E

References

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