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

On the interlacing property and the Routh-Hurwitz criterion

Ziad Zahreddine

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 Ziad Zahreddine. 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.


Unlike the Nyquist criterion, root locus, and many other stability criteria, the well-known Routh-Hurwitz criterion is usually introduced as a mechanical algorithm and no attempt is made whatsoever to explain why or how such an algorithm works. It is widely believed that simple derivations of this important criterion 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 the interlacing property. Within the same context, the singularities that may arise in the Routh-Hurwitz criterion are also dealt with.