On generalization of classical Hurwitz stability criteria for matrix polynomials
On generalization of classical Hurwitz stability criteria for matrix polynomials
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DOI：
10.1016/j.cam.2020.113113
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
X. Zhan;A. Dyachenko
中科院分区：
文献类型：
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作者：
X. Zhan;A. Dyachenko
本文将一类Hurwitz矩阵多项式与Stieltjes正定矩阵列联系起来。这种连接导致的扩展的两个经典标准的赫尔维茨稳定性的真实的多项式矩阵多项式：赫尔维茨稳定性测试通过正定块汉克尔矩阵建立从matricial马尔可夫参数和通过matricial Stieltjes连续分数。我们得到了进一步的条件Hurwitz稳定的块Hankel未成年人和quasimenor，这可能被视为一个弱版本的总积极性准则。
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.