Some remarks on the Ω -stability for families of polynomials

Jean Mawhin

Archivum Mathematicum (1997)

  • Volume: 033, Issue: 1-2, page 139-145
  • ISSN: 0044-8753

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Mawhin, Jean. "Some remarks on the $\Omega $-stability for families of polynomials." Archivum Mathematicum 033.1-2 (1997): 139-145. <http://eudml.org/doc/248036>.

@article{Mawhin1997,
author = {Mawhin, Jean},
journal = {Archivum Mathematicum},
keywords = {Routh-Hurwitz stability; Schur-Cohn stability; Brouwer degree; families of polynomials; zero exclusion principle},
language = {eng},
number = {1-2},
pages = {139-145},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some remarks on the $\Omega $-stability for families of polynomials},
url = {http://eudml.org/doc/248036},
volume = {033},
year = {1997},
}

TY - JOUR
AU - Mawhin, Jean
TI - Some remarks on the $\Omega $-stability for families of polynomials
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 1-2
SP - 139
EP - 145
LA - eng
KW - Routh-Hurwitz stability; Schur-Cohn stability; Brouwer degree; families of polynomials; zero exclusion principle
UR - http://eudml.org/doc/248036
ER -

References

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  1. Anagnost J.J., Desoer C.A., and Minnichelli R.J., Generalized Nyquist tests for robust stability: Frequency domain generalizations of Kharitonov’s theorem, in Robustness in Identification and Control, Milanese, Tempo and Vicino ed., Plenum Press, New York, 1989, 79-96. (1989) MR1041090
  2. Coppel W.A., Stability and Asymptotic Behavior of Differential Equations, Heath, Boston, 1965. (1965) Zbl0154.09301MR0190463
  3. Krein M.G., and Naimark M.A., The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations, Linear and Multilinear Algebra 10 (1981), 265-308. (1981) MR0638124
  4. Lloyd N.G., Degree Theory, Cambridge University Press, Cambridge, 1978. (1978) Zbl0367.47001MR0493564
  5. Marden M., Geometry of Polynomials, American Math. Soc. Providence, RI, 1966. (1966) Zbl0162.37101MR0225972
  6. Rantzer A., Parametric Uncertainty and Feedback Complexity in Linear Control Systems, PhD. Thesis Kungl Tekniska Högskolan, ISRN KHT/OPT SYST/DA-91/13-SE, 1991. (1991) MR2714552
  7. Schur I., Über Potenzreihen, die im Innern des Einheitskreises beschrankt sind, J. Reine Angew. Math. 148 (1918), 122-145. (1918) 
  8. Schur I., Über algebraische Gleichungen, die nur Wurzeln mit negativen Realteilen besitzen, Z. Angew. Math. Mech. 1 (1921), 307-311. (1921) 
  9. Zahreddine Z., On the Γ -stability of systems of differential equations in the Routh-Hurwitz and the Schur-Cohn cases, Bull. Belgian Math. Soc.-Simon Stevin 3 (1996), 363-368. (1996) Zbl0856.34061MR1408281

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