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arXiv · 1711.04651

Total nonnegativity of finite Hurwitz matrices and root location of polynomials

Mohammad Adm·Jürgen Garloff·Mikhail Tyaglov
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Abstract

In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the \emph{closed} left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detail, and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite Hurwitz matrix.

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Mohammad Adm, Jürgen Garloff, Mikhail Tyaglov. 2017-11-09. Total nonnegativity of finite Hurwitz matrices and root location of polynomials. https://doi.org/10.1016/j.jmaa.2018.06.065

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