On generalization of classical Hurwitz stability criteria for matrix polynomials

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:383

Article

Zhan, Xuzhou¹  Dyachenko, Alexander² 

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

[2] UCL, Dept Math, Gower St, London WC1E 6BT, England

关键词: Hurwitz stability;    Stieltjes moment problem;    Markov parameters;    Hankel matrices;    Total positivity;    Quasideterminants;   

DOI  :  10.1016/j.cam.2020.113113

来源: Elsevier

【 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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free