Subclasses of Herglotz-Nevanlinna matrix-valued functions and linear systems

Daniel Alpay, Eduard Tsekanovskii

Research output: Contribution to conferencePaperpeer-review

8 Scopus citations

Abstract

We study Herglotz-Nevanlinna matrix-valued functions that are linear-fractional transformations of the transfer matrix-valued functions of some type of linear, stationary dynamical systems. We introduce the family Fκ of Herglotz-Nevanlinna matrix-valued functions N such that the associated kernel N(Z)-N(w)/z-w N(w)-N(z)/κ is positive in the open upper half-plane. We characterize these functions in terms of Schur functions. This allows us to solve the bitangential interpolation problem in the class Fκ Finally, we consider an associated automorphism of rational unitary functions using state space methods.

Original languageEnglish
Pages1-13
Number of pages13
StatePublished - 1 Jan 2001
Event2000 International Conference on Dynamical Systems and Differential Equations - Atlanta, GA, United States
Duration: 18 May 200021 May 2000

Conference

Conference2000 International Conference on Dynamical Systems and Differential Equations
Country/TerritoryUnited States
CityAtlanta, GA
Period18/05/0021/05/00

ASJC Scopus subject areas

  • Engineering (all)
  • Control and Optimization
  • Discrete Mathematics and Combinatorics

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