On the interlacing property and the Routh-Hurwitz criterionReport as inadecuate




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RETRACTED This article has been retracted as it is found to contain a substantial amount of material from the paper -An Elementary Derivation of the Routh-Hurwitz Criterion,- authored by M. T. Ho, A. Datta and S. P. Bhathacharyya and it is published in -IEEE Transactions on Automatic Control- in 1998.

International Journal of Mathematics and Mathematical Sciences - Volume 2003 2003, Issue 12, Pages 727-737

Department of Basic Sciences, College of Arts and Science, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates

Received 30 May 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Unlike the Nyquist criterion, root locus, and many otherstability criteria, the well-known Routh-Hurwitz criterion isusually introduced as a mechanical algorithm and no attempt ismade whatsoever to explain why or how such an algorithm works. Itis widely believed that simple derivations of this importantcriterion are highly requested by the mathematical community. In this paper, we address this problem and provide a simple proof of the Routh-Hurwitz criterion based on two generalizations of an interesting property known in stability theory as theinterlacing property. Within the same context, the singularitiesthat may arise in the Routh-Hurwitz criterion are also dealt with.





Author: Ziad Zahreddine

Source: https://www.hindawi.com/



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