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Noncommutative rational functions, their difference-differential calculus and realizations

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Drexel University, 3141 Chestnut Str., Philadelphia, PA, 19104, USA

    Dmitry S. Kaliuzhnyi-Verbovetskyi

  2. Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel

    Victor Vinnikov

Authors
  1. Dmitry S. Kaliuzhnyi-Verbovetskyi
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  2. Victor Vinnikov
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Correspondence to Dmitry S. Kaliuzhnyi-Verbovetskyi.

Additional information

Part of the research described in this paper was carried during the first author’s visit to Ben-Gurion University in December 2009 that was partially supported by the Center for Advanced Studies in Mathematics. The revised version was prepared during the stay of the authors in May 2010 at the Mathematisches Forschungs-institut Oberwolfach under the program Research in Pairs. The first author was also supported by the NSF grant DMS 0901628. The research of the second author was partially supported by the Israel Science Foundation.

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Kaliuzhnyi-Verbovetskyi, D.S., Vinnikov, V. Noncommutative rational functions, their difference-differential calculus and realizations. Multidim Syst Sign Process 23, 49–77 (2012). https://doi.org/10.1007/s11045-010-0122-3

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  • DOI: https://doi.org/10.1007/s11045-010-0122-3

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