Riccati inequalities and reproducing kernel Hilbert spaces

Chen Dubi, Harry Dym

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Natural connections between positive semidefinite solutions X of homogeneous algebraic Riccati equations and finite dimensional reproducing kernel de Branges spaces based on a J-inner proper rational square matrix valued functions are known. In this paper analogous connections between the positive semidefinite solutions X of nonhomogeneous algebraic Riccati equations and finite dimensional reproducing kernel Hilbert spaces based on rectangular (J, over(J, ∼))-coinner proper rational matrix valued functions Θ(λ) are developed and are then applied to obtain factorization formulas for Θ(λ) in terms of elementary factors. Enroute, formulas for the factors in a version of a theorem of Leech are also obtained.

Original languageEnglish
Pages (from-to)458-482
Number of pages25
JournalLinear Algebra and Its Applications
Volume420
Issue number2-3
DOIs
StatePublished - 15 Jan 2007
Externally publishedYes

Keywords

  • Factorization
  • Nonhomogeneous Riccati equations
  • Rectangular (J, over(J, ∼))-coinner matrix valued functions
  • Reproducing kernels

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