Quantitatively hyper-positive real rational functions II

Daniel Alpay, Izchak Lewkowicz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Colloquially, quantitatively Hyper-Positive functions form a sub-family of the “Strictly Positive real” functions, where in addition state-space realization always exists and the limit at infinity is non-singular. In scalar terminology, such function maps the right-half of the complex plane into a sub-region of the right-half plane, which can be contained in a finite disk. Moreover, under inversion this disk is mapped onto itself. In [9] we showed that these functions appear in the “absolute stability” Lurie-type problems and characterized these families through their state-space realization, in the spirit of the Kalman-Yakubovich-Popov Lemma. Here, we present additional characterizations, i.e. as rational functions and through the corresponding kernels. Subsequently, a description of all solutions of the tangential Nevanlinna-Pick interpolation problem, in this framework, is presented.

Original languageEnglish
JournalLinear Algebra and Its Applications
StateAccepted/In press - 1 Jan 2024


  • Absolute stability
  • Hyper-positive functions
  • Invertible disks
  • Matrix-convex invertible set
  • Matrix-convex set
  • Nevanlinna-Pick interpolation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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