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
AN - SCOPUS:84855801617
VL - 23
SP - 49
EP - 77
JO - Multidimensional Systems and Signal Processing
JF - Multidimensional Systems and Signal Processing
SN - 0923-6082
IS - 1-2
ER -