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Model reduction of time-delay systems using position balancing and delay Lyapunov equations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0001-9443-8772
2013 (English)In: MCSS. Mathematics of Control, Signals and Systems, ISSN 0932-4194, E-ISSN 1435-568X, Vol. 25, no 2, 147-166 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2013. Vol. 25, no 2, 147-166 p.
Keyword [en]
Time-delay systems, Model reduction, Balanced truncation, Lyapunov equations
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-123143DOI: 10.1007/s00498-012-0096-9ISI: 000317986300001ScopusID: 2-s2.0-84882664013OAI: diva2:624674
Swedish eā€Science Research Center

QC 20130603

Available from: 2013-06-03 Created: 2013-06-03 Last updated: 2013-06-03Bibliographically approved

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Jarlebring, Elias
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Numerical Analysis, NA
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