On Bézoutians, Van der Monde matrices, and the Lienard-Chipart stability criterion

DOI10.1016/0024-3795(89)90367-4zbMath0677.15011OpenAlexW2164950942MaRDI QIDQ1123238

Paul A. Fuhrmann, Biswa N. Datta

Publication date: 1989

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(89)90367-4

zbMATH Keywords

Hurwitz polynomialBézoutiandiagonal formLienard-Chipart stability criterionVan der Monde matrices

Mathematics Subject Classification ID

Asymptotic stability in control theory (93D20) Hermitian, skew-Hermitian, and related matrices (15B57) Quadratic and bilinear forms, inner products (15A63)

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Cites Work

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• Algebraic system theory: An analyst's point of view
• On the Routh-Hurwitz-Fujiwara and the Schur-Cohn-Fujiwara theorems for the root-separation problem
• An elementary proof of the stability criterion of Lienard and Chipart
• Bézoutians
• The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations
• Duality in polynomial models with some applications to geometric control theory