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On the interlacing property and the Routh-Hurwitz criterion

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  • Ziad Zahreddine

Abstract

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.

Suggested Citation

  • Ziad Zahreddine, 2003. "On the interlacing property and the Routh-Hurwitz criterion," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-11, January.
  • Handle: RePEc:hin:jijmms:624382
    DOI: 10.1155/S0161171203205287
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    1. Sikazwe, Geofrey & Yocgo, Rosita E.E. & Landi, Pietro & Richardson, David M. & Hui, Cang, 2024. "Managing whitefly development to control cassava brown streak virus coinfections," Ecological Modelling, Elsevier, vol. 493(C).

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