On generalization of classical Hurwitz stability criteria for matrix polynomials

Xuzhou Zhan, Alexander Dyachenko

备注：: 26 pages
DOI：: 10.1016/j.cam.2020.113113

英文摘要：

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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