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 language | English |
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Pages (from-to) | 257-271 |
Journal | IEEE Transactions on Automatic Control |
Volume | 68 |
Issue number | 1 |
DOIs | |
Publication status | Published - 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-careOtherwise 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