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A generalized Hurwitz stability criterion via rectangular block Hankel matrices for nonmonic matrix polynomials

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Název: A generalized Hurwitz stability criterion via rectangular block Hankel matrices for nonmonic matrix polynomials
Autoři: Ni, Zixiang, Hu, Yongjian, Zhan, Xuzhou
Rok vydání: 2025
Sbírka: ArXiv.org (Cornell University Library)
Témata: Optimization and Control, Numerical Analysis
Popis: We develop a Hurwitz stability criterion for nonmonic matrix polynomials via column reduction, generalizing existing approaches constrained by the monic assumption and thus serving as a more natural extension of Gantmacher's classical stability criterion via Markov parameters. Starting from redefining the associated Markov parameters through a column-wise adaptive splitting method, our framework constructs two structured matrices whose rectangular Hankel blocks are obtained via the extraction of these parameters. We establish an explicit interrelation between the inertias of column reduced matrix polynomials and the derived structured matrices. Furthermore, we demonstrate that the Hurwitz stability of column reduced matrix polynomials can be determined by the Hermitian positive definiteness of these rectangular block Hankel matrices.
Druh dokumentu: text
Jazyk: unknown
Relation: http://arxiv.org/abs/2508.14376
Dostupnost: http://arxiv.org/abs/2508.14376
Přístupové číslo: edsbas.B85A359E
Databáze: BASE
Popis
Abstrakt:We develop a Hurwitz stability criterion for nonmonic matrix polynomials via column reduction, generalizing existing approaches constrained by the monic assumption and thus serving as a more natural extension of Gantmacher's classical stability criterion via Markov parameters. Starting from redefining the associated Markov parameters through a column-wise adaptive splitting method, our framework constructs two structured matrices whose rectangular Hankel blocks are obtained via the extraction of these parameters. We establish an explicit interrelation between the inertias of column reduced matrix polynomials and the derived structured matrices. Furthermore, we demonstrate that the Hurwitz stability of column reduced matrix polynomials can be determined by the Hermitian positive definiteness of these rectangular block Hankel matrices.