On generalization of classical Hurwitz stability criteria for matrix polynomials
Classical Analysis and ODEs
2020-08-14 v1 Spectral Theory
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.
Keywords
Cite
@article{arxiv.1909.13402,
title = {On generalization of classical Hurwitz stability criteria for matrix polynomials},
author = {Xuzhou Zhan and Alexander Dyachenko},
journal= {arXiv preprint arXiv:1909.13402},
year = {2020}
}
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26 pages