Noncommutative rational functions, their difference-differential calculus and realizations

Authors:
Dmitry S. Kaliuzhnyi-Verbovetskyi;Victor Vinnikov
Affiliations:
Department of Mathematics, Drexel University, Philadelphia, USA 19104;Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel 84105
Venue:
Multidimensional Systems and Signal Processing
Year:
2012

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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.