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Model reduction of time-delay systems using position balancing and delay Lyapunov equations

Titelangaben

Jarlebring, Elias ; Damm, Tobias ; Michiels, Wim:
Model reduction of time-delay systems using position balancing and delay Lyapunov equations.
In: Mathematics of Control, Signals, and Systems. Bd. 25 (2013) Heft 2 . - S. 147-166.
ISSN 0932-4194
DOI: https://doi.org/10.1007/s00498-012-0096-9

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Projekttitel:
Offizieller Projekttitel
Projekt-ID
Programme of Interuniversity Attraction Poles
IAP P6-DYSCO
Optimization in Engineering Center (OPTEC)
Ohne Angabe
Project
STRT1-09/33
Dahlquist research fellowship
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Projektfinanzierung: Belgian Federal Science Policy Office
K.U. Leuven
K.U. Leuven Research Council
Royal Institute of Technology (KTH) in Stockholm, Sweden

Abstract

Balanced truncation is a standard and very natural approach to approximate dynamical systems. We present a version of balanced truncation for model order reduction of linear time-delay systems. The procedure is based on a coordinate transformation of the position and preserves the delay structure of the system. We therefore call it (structure-preserving) position balancing. To every position, we associate quantities representing energies for the controllability and observability of the position. We show that these energies can be expressed explicitly in terms of the solutions to corresponding delay Lyapunov equations. Apart from characterizing the energies, we show that one block of the (operator) controllability and observability Gramians in the operator formulation of the time-delay system can also be characterized with the delay Lyapunov equation. The delay Lyapunov equation undergoes a contragredient transformation when we apply the position coordinate transformation and we propose to truncate it in a classical fashion, such that positions which are only weakly connected to the input and the output in the sense of the energy concepts are removed.

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Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Keywords: time-delay systems; model reduction; balanced truncation; Lyapunov equations
Fachklassifikationen: Mathematics Subject Classification Code: 93B11 (93C23 93D30)
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Angewandte Mathematik (Angewandte Mathematik)
Profilfelder > Advanced Fields > Nichtlineare Dynamik
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Profilfelder
Profilfelder > Advanced Fields
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 24 Mär 2015 09:13
Letzte Änderung: 24 Mär 2015 09:13
URI: https://eref.uni-bayreuth.de/id/eprint/9250