Extended balancing of continuous LTI systems: a structure-preserving approach

Pablo Borja, Jacquelien M.A. Scherpen, Kenji Fujimoto

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
8 Downloads (Pure)

Abstract

In this article, we treat extended balancing for continuous-time linear time-invariant systems. We take a dissipativity perspective, thus, resulting in a characterization in terms of linear matrix inequalities. This perspective is useful for determining a priori error bounds. In addition, we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model. We illustrate the results with a large-scale mechanical system example. Furthermore, we show how to interpret a reduced-order model of an electrical circuit again as a lower dimensional electrical circuit.

Original languageEnglish
Pages (from-to)257-271
JournalIEEE Transactions on Automatic Control
Volume68
Issue number1
DOIs
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • Controllability
  • error bound
  • extended Gramians
  • Linear matrix inequalities
  • Linear systems
  • model reduction
  • Observability
  • port-Hamiltonian systems
  • Reduced order systems
  • Standards
  • Symmetric matrices

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