TY - JOUR

T1 - An elementary derivation of the Routh-Hurwitz criterion

AU - Ho, Ming Tzu

AU - Datta, Aniruddha

AU - Bhattacharyya, S. P.

N1 - Funding Information:
Manuscript received January 31, 1996. This work was supported in part by the National Science Foundation under Grant ECS-9417004 and by the Texas Advanced Technology Program under Grant 999903-002. The authors are with the Department of Electrical Engineering, Texas A & M University, College Station, TX 77843-3128 USA. Publisher Item Identifier S 0018-9286(98)01441-X.

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

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U2 - 10.1109/9.661607

DO - 10.1109/9.661607

M3 - Article

AN - SCOPUS:0032022795

SN - 0018-9286

VL - 43

SP - 405

EP - 409

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 3

ER -