On the computation of the Cauchy index
Author:
Brian D. O. Anderson
Journal:
Quart. Appl. Math. 29 (1972), 577-582
MSC:
Primary 93B25
DOI:
https://doi.org/10.1090/qam/403746
MathSciNet review:
403746
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Abstract: The Cauchy index of a real rational function can be computed by evaluating the signature of a certain Hankel matrix. Alternative procedures for its computation are presented here, one of which offers greater computational simplicity.
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L. A. Zadeh and C. A. Desoer, Linear system theory, McGraw-Hill, New York, 1963
C. Hermite, Sur le nombre des racines d’une équation algébrique comprise entre des limites données, J. Reine Angew. Math. 52, 39–51, (1854) and Oeuvres 1, pp. 397–414
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B. D. O. Anderson, Application of the second method of Lyapunov to the proof of the Markov stability criterion, Internat. J. Control. 5, 473–482 (1967)
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- A. S. Householder, Bezoutiants, elimination and localization, SIAM Rev. 12 (1970), 73–78. MR 272181, DOI https://doi.org/10.1137/1012003
W. Jarominek, Investigating linear systems of automatic control by means of determinant stability margin indices, Proc. First IFAC Congress 1, 76–84, Butterworths, London, 1961
- Vlasislav Jarominek, The equivalence of the Routh-Hurwitz and the Markov stability criteria, Soviet Physics Dokl. 5 (1960), 78–82. MR 0139808
F. R. Gantmacher, The theory of matrices, Chelsea, New York, 1959
L. A. Zadeh and C. A. Desoer, Linear system theory, McGraw-Hill, New York, 1963
C. Hermite, Sur le nombre des racines d’une équation algébrique comprise entre des limites données, J. Reine Angew. Math. 52, 39–51, (1854) and Oeuvres 1, pp. 397–414
P. C. Parks, A new proof of the Routh-Hurwitz stability criterion using the second method of Lyapunov, Proc. Cambridge Philos. Soc. 58, part 4, pp. 694–702 (1962)
B. D. O. Anderson, Application of the second method of Lyapunov to the proof of the Markov stability criterion, Internat. J. Control. 5, 473–482 (1967)
R. E. Kalman, On the Hermite-Fujiwara theorem in stability theory, Quart. Appl. Math. 23, 279–282 (1965)
A. S. Householder, Bezoutiants, elimination and localization, SIAM Rev. 12, 73–78 (1970)
W. Jarominek, Investigating linear systems of automatic control by means of determinant stability margin indices, Proc. First IFAC Congress 1, 76–84, Butterworths, London, 1961
W. Jarominek, The equivalence of the Routh-Hurwitz and the Markov stability criteria, Soviet Physics Dokl. 5, 78–82 (1960)
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Article copyright:
© Copyright 1972
American Mathematical Society
