Total nonnegativity of finite Hurwitz matrices and root location of polynomials
arXiv:1711.04651 · doi:10.1016/j.jmaa.2018.06.065
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.
arXiv comment20 pages. arXiv admin note: text overlap with arXiv:1005.3032
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