Noncommutative rational functions, their difference-differential calculus and realizations

Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


Noncommutative rational functions appeared in many contexts in system theory and control, from the theory of finite automata and formal languages to robust control and LMIs. We survey the construction of noncommutative rational functions, their realization theory and some of their applications. We also develop a difference-differential calculus as a tool for further analysis.

Original languageEnglish
Pages (from-to)49-77
Number of pages29
JournalMultidimensional Systems and Signal Processing
Issue number1-2
StatePublished - 1 Jun 2012


  • Directional derivatives
  • Noncommutative backward shifts
  • Noncommutative difference-differential calculus
  • Noncommutative formal power series
  • Noncommutative polynomials
  • Noncommutative rational functions
  • Noncommutative realization theory
  • Skew fields of fractions
  • Structured noncommutative multidimensional linear systems

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Information Systems
  • Hardware and Architecture
  • Computer Science Applications
  • Artificial Intelligence
  • Applied Mathematics


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