Noncommutative rational functions, their difference-differential calculus and realizations

Dmitry S. Kaliuzhnyi-Verbovetskyi; Victor Vinnikov

doi:10.1007/s11045-010-0122-3

Noncommutative rational functions, their difference-differential calculus and realizations

Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Pages (from-to)	49-77
Number of pages	29
Journal	Multidimensional Systems and Signal Processing
Volume	23
Issue number	1-2
DOIs	https://doi.org/10.1007/s11045-010-0122-3
State	Published - 1 Jun 2012

Keywords

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

All Science Journal Classification (ASJC) codes

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

Access to Document

10.1007/s11045-010-0122-3

Cite this

@article{0f373ec07a074a66a284fbe0f025a053,

title = "Noncommutative rational functions, their difference-differential calculus and realizations",

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.",

keywords = "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",

author = "Kaliuzhnyi-Verbovetskyi, {Dmitry S.} and Victor Vinnikov",

note = "Funding Information: Part of the research described in this paper was carried during the first author{\textquoteright}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.",

year = "2012",

month = jun,

day = "1",

doi = "10.1007/s11045-010-0122-3",

language = "American English",

volume = "23",

pages = "49--77",

journal = "Multidimensional Systems and Signal Processing",

issn = "0923-6082",

publisher = "Springer Netherlands",

number = "1-2",

}

TY - JOUR

T1 - Noncommutative rational functions, their difference-differential calculus and realizations

AU - Kaliuzhnyi-Verbovetskyi, Dmitry S.

AU - Vinnikov, Victor

N1 - Funding 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.

PY - 2012/6/1

Y1 - 2012/6/1

N2 - 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.

AB - 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.

KW - Directional derivatives

KW - Noncommutative backward shifts

KW - Noncommutative difference-differential calculus

KW - Noncommutative formal power series

KW - Noncommutative polynomials

KW - Noncommutative rational functions

KW - Noncommutative realization theory

KW - Skew fields of fractions

KW - Structured noncommutative multidimensional linear systems

UR - http://www.scopus.com/inward/record.url?scp=84855801617&partnerID=8YFLogxK

U2 - 10.1007/s11045-010-0122-3

DO - 10.1007/s11045-010-0122-3

M3 - Article

SN - 0923-6082

VL - 23

SP - 49

EP - 77

JO - Multidimensional Systems and Signal Processing

JF - Multidimensional Systems and Signal Processing

IS - 1-2

ER -

Noncommutative rational functions, their difference-differential calculus and realizations

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this