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Volumn 371, Issue SUPPL., 2003, Pages 105-110

Hermite-Biehler, Routh-Hurwitz, and total positivity

Author keywords

Hermite Biehler theorem; Hurwitz matrix; Root interlacing; Routh Hurwitz criterion; Stability; Totally nonnegative matrices

Indexed keywords

GRAPH THEORY; MATRIX ALGEBRA; POLYNOMIALS; THEOREM PROVING; ALGORITHMS; PROBLEM SOLVING; ROOT LOCI;

EID: 0142260589     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(03)00501-9     Document Type: Article
Times cited : (51)

References (19)
  • 1
    • 0025956334 scopus 로고
    • An elementary proof of the Routh-Hurwitz stability criterion
    • Anagnost J.J., Desoer C.A. An elementary proof of the Routh-Hurwitz stability criterion. Circuits Systems Signal Process. 10(1):1991;101-114.
    • (1991) Circuits Systems Signal Process , vol.10 , Issue.1 , pp. 101-114
    • Anagnost, J.J.1    Desoer, C.A.2
  • 2
    • 0014749705 scopus 로고
    • On the total nonnegativity of the Hurwitz matrix
    • Asner B.A. On the total nonnegativity of the Hurwitz matrix. SIAM J. Appl. Math. 18:1970;407-414.
    • (1970) SIAM J. Appl. Math. , vol.18 , pp. 407-414
    • Asner, B.A.1
  • 3
    • 30644462427 scopus 로고
    • Sur une classe d'équations algébriques dont toutes les racines sont réelles
    • Biehler M. Sur une classe d'équations algébriques dont toutes les racines sont réelles. J. Reine Angew. Math. 87:1879;350-352.
    • (1879) J. Reine Angew. Math. , vol.87 , pp. 350-352
    • Biehler, M.1
  • 4
    • 0000463168 scopus 로고
    • Routh's algorithm: A centennial survey
    • Barnett S., Siljak D.D. Routh's algorithm: a centennial survey. SIAM Rev. 19(3):1977;472-489.
    • (1977) SIAM Rev. , vol.19 , Issue.3 , pp. 472-489
    • Barnett, S.1    Siljak, D.D.2
  • 5
    • 3543063597 scopus 로고
    • The Routh-Hurwitz problem for polynomials and entire functions: Real quasipolynomials with r = 3, s = 1
    • G.S. Barhin, A.N. Hovanskii (Eds.), (in Russian)
    • N.G. Chebotarev, N.N. Meiman, The Routh-Hurwitz problem for polynomials and entire functions: real quasipolynomials with r=3, s=1, in: G.S. Barhin, A.N. Hovanskii (Eds.), Tr. Mat. Inst. Steklova, vol. 26, 1949 (in Russian).
    • (1949) Tr. Mat. Inst. Steklova , vol.26
    • Chebotarev, N.G.1    Meiman, N.N.2
  • 6
    • 84966236381 scopus 로고
    • On the zeros of polynomials with complex coefficients
    • Frank E. On the zeros of polynomials with complex coefficients. Bull. Amer. Math. Soc. 52:1946;144-157.
    • (1946) Bull. Amer. Math. Soc. , vol.52 , pp. 144-157
    • Frank, E.1
  • 8
    • 21444442455 scopus 로고    scopus 로고
    • Euclid algorithm, orthogonal polynomials, and generalized Routh-Hurwitz algorithm
    • Genin Y.V. Euclid algorithm, orthogonal polynomials, and generalized Routh-Hurwitz algorithm. Linear Algebra Appl. 246:1996;131-158.
    • (1996) Linear Algebra Appl. , vol.246 , pp. 131-158
    • Genin, Y.V.1
  • 9
    • 0011452575 scopus 로고
    • Sur les nombre des racines d'une équation algébrique comprise entre des limites données
    • Hermite C. Sur les nombre des racines d'une équation algébrique comprise entre des limites données. J. Reine Angew. Math. 52:1856;39-51.
    • (1856) J. Reine Angew. Math. , vol.52 , pp. 39-51
    • Hermite, C.1
  • 10
    • 0014707063 scopus 로고
    • Bezoutians, elimination and localization
    • Householder A.S. Bezoutians, elimination and localization. SIAM Rev. 12(1):1970;73-78.
    • (1970) SIAM Rev. , vol.12 , Issue.1 , pp. 73-78
    • Householder, A.S.1
  • 11
    • 0001440029 scopus 로고
    • Über die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Teilen besitzt
    • Hurwitz A. Über die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Teilen besitzt. Math. Ann. 46:1895;273-284.
    • (1895) Math. Ann. , vol.46 , pp. 273-284
    • Hurwitz, A.1
  • 12
    • 0000602606 scopus 로고
    • A Hurwitz matrix is totally positive
    • Kemperman J.H.B. A Hurwitz matrix is totally positive. SIAM J. Math. Anal. 13:1982;331-341.
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 331-341
    • Kemperman, J.H.B.1
  • 13
    • 0002225475 scopus 로고
    • The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations
    • Krein M.G., 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) Linear and Multilinear Algebra , vol.10 , pp. 265-308
    • Krein, M.G.1    Naimark, M.A.2
  • 14
    • 0029345508 scopus 로고
    • Elementary proof of the Routh-Hurwitz test
    • Meinsma G. Elementary proof of the Routh-Hurwitz test. Systems Control Lett. 25(4):1995;237-242.
    • (1995) Systems Control Lett. , vol.25 , Issue.4 , pp. 237-242
    • Meinsma, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.