Hurwitz rational functions
A generalization of Hurwitz stable polynomials to real rational functions is considered. We establish an analog of the Hurwitz stability criterion for rational functions and introduce a new type of determinants that can be treated as a generalization of the Hurwitz determinants.
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| Veröffentlicht in: | Linear algebra and its applications Jg. 435; H. 8; S. 1845 - 1856 |
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| Sprache: | Englisch |
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15.10.2011
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| ISSN: | 0024-3795 |
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| Abstract | A generalization of Hurwitz stable polynomials to real rational functions is considered. We establish an analog of the Hurwitz stability criterion for rational functions and introduce a new type of determinants that can be treated as a generalization of the Hurwitz determinants. |
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| AbstractList | A generalization of Hurwitz stable polynomials to real rational functions is considered. We establish an analog of the Hurwitz stability criterion for rational functions and introduce a new type of determinants that can be treated as a generalization of the Hurwitz determinants. |
| Author | Tyaglov, Mikhail Barkovsky, Yury |
| Author_xml | – sequence: 1 givenname: Yury surname: Barkovsky fullname: Barkovsky, Yury organization: Department of Calculus Mathematics and Mathematical Physics, Faculty of Mathematics, Mechanics & Computer Science, Southern Federal University, Milchakova str. 8a, 344090 Rostov-on-Don, Russia – sequence: 2 givenname: Mikhail surname: Tyaglov fullname: Tyaglov, Mikhail email: tyaglov@math.tu-berlin.de organization: Technische Universität Berlin, Institut für Mathematik, MA 4-5, Strasse des 17. Juni 136, 10623 Berlin, Germany |
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| Cites_doi | 10.1007/BF01446812 |
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| Copyright | 2011 Elsevier Inc. |
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| Issue | 8 |
| Keywords | Pole localization Hurwitz stable polynomials Root localization 26C10 Hurwitz rational function Hurwitz matrix 15B05 26C15 15A15 26C05 30C15 |
| Language | English |
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| References | O. Holtz, M. Tyaglov, Structured matrices, continued fractions and root localization of polynomials, SIAM Review 2009, accepted for publication. Available from: arXiv:0912.470. Yu.S. Barkovskiy, Lectures on the Routh–Hurwitz Problem, 2008, in press. Available from Hurwitz (b0020) 1895; 46 Gantmacher (b0010) 2000; vol. II 1936 (in Russian). English transl. M.G. Krein, M.A. Naimark, The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations, Linear and Multilinear Algebra 10 (4) (1981) 265–308. Translated from the Russian by O. Boshko and J.L. Howland. M. Tyaglov, Generalized Hurwitz polynomials, 2010, submitted for publication. Available from: arXiv:1005.3032. . Frobenius (10.1016/j.laa.2011.03.062_fs010) 1894 Gantmacher (10.1016/j.laa.2011.03.062_b0010) 2000; vol. II 10.1016/j.laa.2011.03.062_b0030 Hurwitz (10.1016/j.laa.2011.03.062_b0020) 1895; 46 10.1016/j.laa.2011.03.062_b0005 10.1016/j.laa.2011.03.062_b0015 10.1016/j.laa.2011.03.062_b0025 |
| References_xml | – reference: M. Tyaglov, Generalized Hurwitz polynomials, 2010, submitted for publication. Available from: arXiv:1005.3032. – reference: O. Holtz, M. Tyaglov, Structured matrices, continued fractions and root localization of polynomials, SIAM Review 2009, accepted for publication. Available from: arXiv:0912.470. – reference: Yu.S. Barkovskiy, Lectures on the Routh–Hurwitz Problem, 2008, in press. Available from: – volume: vol. II year: 2000 ident: b0010 publication-title: The Theory of Matrices – volume: 46 start-page: 273 year: 1895 end-page: 284 ident: b0020 article-title: Über die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt publication-title: Math. Ann. – reference: ▪ ▪, 1936 (in Russian). English transl. M.G. Krein, M.A. Naimark, The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations, Linear and Multilinear Algebra 10 (4) (1981) 265–308. Translated from the Russian by O. Boshko and J.L. Howland. – reference: . – start-page: 241 year: 1894 ident: 10.1016/j.laa.2011.03.062_fs010 article-title: Über das Trägheitsgesetz der quadratischen Formen publication-title: Sitzungsber. Ber. Acad. Wiss. Phys. Math. Klasse Berlin – ident: 10.1016/j.laa.2011.03.062_b0025 – ident: 10.1016/j.laa.2011.03.062_b0005 – ident: 10.1016/j.laa.2011.03.062_b0030 – volume: vol. II year: 2000 ident: 10.1016/j.laa.2011.03.062_b0010 – ident: 10.1016/j.laa.2011.03.062_b0015 – volume: 46 start-page: 273 year: 1895 ident: 10.1016/j.laa.2011.03.062_b0020 article-title: Über die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt publication-title: Math. Ann. doi: 10.1007/BF01446812 |
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| SubjectTerms | Hurwitz matrix Hurwitz rational function Hurwitz stable polynomials Pole localization Root localization |
| Title | Hurwitz rational functions |
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