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

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

Research output: Contribution to journalArticleScientificpeer-review


In this paper, 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
JournalIEEE Transactions on Automatic Control
Publication statusAccepted/In press - 2022

Bibliographical note

Accepted Author Manuscript


  • 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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