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arXiv · 1909.13402

On generalization of classical Hurwitz stability criteria for matrix polynomials

Xuzhou Zhan·Alexander Dyachenko
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Abstract

In this paper, we associate a class of Hurwitz matrix polynomials with Stieltjes positive definite matrix sequences. This connection leads to an extension of two classical criteria of Hurwitz stability for real polynomials to matrix polynomials: tests for Hurwitz stability via positive definiteness of block-Hankel matrices built from matricial Markov parameters and via matricial Stieltjes continued fractions. We obtain further conditions for Hurwitz stability in terms of block-Hankel minors and quasiminors, which may be viewed as a weak version of the total positivity criterion.

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BibTeXRIS

Xuzhou Zhan, Alexander Dyachenko. 2019-09-30. On generalization of classical Hurwitz stability criteria for matrix polynomials. https://doi.org/10.1016/j.cam.2020.113113

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