Composition of rational functions: State-space realization and applications

Daniel Alpay, Izchak Lewkowicz

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the original functions. Focusing on positive real functions, the first composition is applied to electrical circuits theory along with introducing a connection to networks of feedback loops. The second composition is applied to Stieltjes functions.

Original languageEnglish
Pages (from-to)359-383
Number of pages25
JournalLinear Algebra and Its Applications
StatePublished - 1 Nov 2019


  • Composition
  • Convex invertible cones
  • Electrical circuits
  • Feedback loops
  • Positive real functions
  • Rational functions of non-commuting variables
  • State-space realization
  • Stieltjes functions

ASJC Scopus subject areas

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


Dive into the research topics of 'Composition of rational functions: State-space realization and applications'. Together they form a unique fingerprint.

Cite this