Title
Extended balancing of continuous LTI systems: a structure-preserving approach
Author
Borja Rosales, L.P. (TU Delft Learning & Autonomous Control)
Scherpen, Jacquelien M.A. (Rijksuniversiteit Groningen)
Fujimoto, Kenji (Kyoto University)
Date
2023
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.
Subject
Controllability
error bound
extended Gramians
Linear matrix inequalities
Linear systems
model reduction
Observability
port-Hamiltonian systems
Reduced order systems
Standards
Symmetric matrices
To reference this document use:
http://resolver.tudelft.nl/uuid:a27efc12-b18d-48a3-9c96-de97c10139df
DOI
https://doi.org/10.1109/TAC.2021.3138645
Embargo date
2023-07-01
ISSN
0018-9286
Source
IEEE Transactions on Automatic Control, 68 (1), 257-271
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.
Part of collection
Institutional Repository
Document type
journal article
Rights
© 2023 L.P. Borja Rosales, Jacquelien M.A. Scherpen, Kenji Fujimoto