On Foster’s theorem and positive para odd functions

Zahreddine, Ziad

doi:10.47974/JIM-1725

Open Access Research Article

On Foster’s theorem and positive para odd functions

^*Ziad ZahreddineCorresponding authorz.zahreddine@kcst.edu.kw ziadzahr@hotmail.comDepartment of MathematicsCollege of EngineeringKuwait College of Science and Technology (KCST)KuwaitView full profile →

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pp. 67–75Vol. 27Issue 1February 2024DOI: 10.47974/JIM-1725XML

Received:: 05 Jan 2023
Published Online:: 27 Feb 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1725
Pages:: 67–75

Abstract

Various tools in the literature are used to enhance the understanding of the Routh-Hurwitz stability theory. Among such tools are Foster’s theorem and positive para odd functions. One of the objectives of this paper is to show strong correlations between these two tools. Such correlations enable us to create simple forms of such functions which can prove useful in tackling stability issues. Also, a simple derivation of Foster’s Theorem is advanced using complex analysis techniques, avoiding the use of circuit network theory which led to Foster’s theorem. A general form of positive and para odd functions is also advanced.

Keywords

Foster’s theorem Positive para odd Routh-Hurwitz algorithm Stability tests

Subject Classifications

(2010) Primary 37C7593C15. Secondary 93D30E

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