Herglotz-Nevanlinna matrix functions and Hurwitz stability of matrix polynomials

2020/06/29 by Xuzhou Zhan, Zhan, Xuzhou
Mathematics · #15A24 #26C15 #30C15 #34D20 #47A56 #93D20 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #math.CA #math.DS #math.OC #msc:15A24 #msc:26C15 #msc:30C15 #msc:34D20 #msc:47A56 #msc:93D20

paper · pdf · doi:10.48550/arxiv.2006.16065

20 pages

arxiv created 2021/03/05 · arxiv updated 2021/03/08

Abstract

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.

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