Model order reduction for linear time delay systems: a delay-dependent approach based on energy functionals

Sajad Naderi Lordejani (Corresponding author), Bart Besselink, Antoine Chaillet, Nathan van de Wouw

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Abstract

This paper proposes a model order reduction technique for asymptotically stable linear time delay systems with point-wise delays. The presented delay-dependent approach, which can be regarded as an extension of existing balancing model order reduction techniques for linear delay-free systems, is based on energy functionals that characterize observability and controllability properties of the time delay system. The reduced model obtained by this approach is an asymptotically stable time delay system of the same type as the original model, meaning that the approach is both stability- and structure-preserving. It also provides an a priori bound on the reduction error, serving as a measure of the reduction accuracy. The effectiveness of the proposed method is illustrated by numerical simulations.

Original languageEnglish
Article number108701
Number of pages10
JournalAutomatica
Volume112
DOIs
Publication statusPublished - Feb 2020

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Time delay
Observability
Controllability
Computer simulation

Keywords

  • model reduction
  • time delay systems
  • linear systems
  • functional
  • matrix inequalities
  • balancing

Cite this

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abstract = "This paper proposes a model order reduction technique for asymptotically stable linear time delay systems with point-wise delays. The presented delay-dependent approach, which can be regarded as an extension of existing balancing model order reduction techniques for linear delay-free systems, is based on energy functionals that characterize observability and controllability properties of the time delay system. The reduced model obtained by this approach is an asymptotically stable time delay system of the same type as the original model, meaning that the approach is both stability- and structure-preserving. It also provides an a priori bound on the reduction error, serving as a measure of the reduction accuracy. The effectiveness of the proposed method is illustrated by numerical simulations.",
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Model order reduction for linear time delay systems : a delay-dependent approach based on energy functionals. / Naderi Lordejani, Sajad (Corresponding author); Besselink, Bart; Chaillet, Antoine; van de Wouw, Nathan.

In: Automatica, Vol. 112, 108701, 02.2020.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - van de Wouw, Nathan

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