An elementary derivation of the Routh-Hurwitz criterion Conference Paper uri icon

abstract

  • In most undergraduate texts on control systems, the Routh-Hurwitz criterion is usually introduced as a mechanical algorithm for determining the Hurwitz stability of a real polynomial. Unlike many other stability criteria such as the Nyquist criterion, root locus, etc. no attempt whatsoever is made to even allude to a proof of the Routh-Hurwitz criterion. Recent result using the Hermite Biehler Theorems have, however, succeeded in providing a simple derivation of Routh's algorithm for determining the Hurwitz stability or otherwise of a given real polynomial. However, this derivation fails to capture the fact that Routh's algorithm can also be used to count the number of open right half plane roots of a given polynomial. This paper shows that by using appropriately generalized versions of the Hermite-Biehler Theorem, it is possible to provide a simple derivation of the Routh-Hurwitz criterion which also captures its unstable root counting capability.

name of conference

  • Proceedings of 35th IEEE Conference on Decision and Control

published proceedings

  • PROCEEDINGS OF THE 35TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4

author list (cited authors)

  • Ho, M. T., Datta, A., & Bhattacharyya, S. P.

citation count

  • 1

complete list of authors

  • Ho, MT||Datta, A||Bhattacharyya, SP

publication date

  • January 1996