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

Title data

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. Vol. 25 (2013) Issue 2 . - pp. 147-166.
ISSN 0932-4194
DOI: https://doi.org/10.1007/s00498-012-0096-9

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Project information

Project title:
Project's official titleProject's id
Programme of Interuniversity Attraction PolesIAP P6-DYSCO
Optimization in Engineering Center (OPTEC)No information
ProjectSTRT1-09/33
Dahlquist research fellowshipNo information

Project financing: Belgian Federal Science Policy Office
K.U. Leuven
K.U. Leuven Research Council
Royal Institute of Technology (KTH) in Stockholm, Sweden

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: time-delay systems; model reduction; balanced truncation; Lyapunov equations
Subject classification: Mathematics Subject Classification Code: 93B11 (93C23 93D30)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 24 Mar 2015 09:13
Last Modified: 24 Mar 2015 09:13
URI: https://eref.uni-bayreuth.de/id/eprint/9250