An elementary derivation of the Routh-Hurwitz criterion

Ming Tzu Ho, Aniruddha Datta, S. P. Bhattacharyya

研究成果: Article同行評審

40 引文 斯高帕斯(Scopus)

摘要

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 results using the Hermite-Biehler theorem 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.

原文English
頁(從 - 到)405-409
頁數5
期刊IEEE Transactions on Automatic Control
43
發行號3
DOIs
出版狀態Published - 1998

All Science Journal Classification (ASJC) codes

  • 控制與系統工程
  • 電腦科學應用
  • 電氣與電子工程

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