论文标题
herglotz-nevanlinna矩阵函数和基质多项式稳定性
Herglotz-Nevanlinna matrix functions and Hurwitz stability of matrix polynomials
论文作者
论文摘要
本文详细阐述了矩阵值的HERGLOTZ-NEVANLINNA函数与Hurwitz稳定矩阵多项式之间的关系，该矩阵多项式概括了相应的经典稳定性标准。主要动机来自作者最近与母系马尔可夫参数相关的稳定研究。为了实现我们的目标，我们首先通过Herglotz-Nevanlinna属性将部分分数分解。下一步是将矩阵值的herglotz-nevanlinna功能与其矩阵laurent系列联系起来。还建立了Chebotarev和Grommer对两个经典定理的某些矩阵扩展。
This paper elaborates on a relationship between matrix-valued Herglotz-Nevanlinna functions and Hurwitz stable matrix polynomials, which generalizes the corresponding classical stability criterion. The main motivation comes from the author's recent stability studies linked with matricial Markov parameters. To fulfill our goals, we first give a partial-fraction decomposition of a self-adjoint rational matrix function with the Herglotz-Nevanlinna property. The next step is to connect a matrix-valued Herglotz-Nevanlinna function with its matricial Laurent series. Certain matrix extensions to two classical theorems by Chebotarev and Grommer, respectively, are also established.
