Quantitatively hyper-positive real functions

Daniel Alpay, Izchak Lewkowicz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Hyper-positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion. A state-space characterization of these functions through a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.

Original languageEnglish
Pages (from-to)316-334
Number of pages19
JournalLinear Algebra and Its Applications
StatePublished - 15 Aug 2021


  • Absolute stability
  • Convex invertible cones
  • Electrical circuits
  • Feedback loops
  • Hyper-positive real functions
  • K-Y-P lemma
  • Matrix-convex set
  • Positive real functions
  • State-space realization

ASJC Scopus subject areas

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


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