Extended balancing of continuous LTI systems

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

Borja Rosales, L.P. (TU Delft Learning & Autonomous Control)
Scherpen, Jacquelien M.A. (Rijksuniversiteit Groningen)
Fujimoto, Kenji (Kyoto University)

2023

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.

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

http://resolver.tudelft.nl/uuid:a27efc12-b18d-48a3-9c96-de97c10139df

https://doi.org/10.1109/TAC.2021.3138645

2023-07-01

0018-9286

IEEE Transactions on Automatic Control, 68 (1), 257-271

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.

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journal article

© 2023 L.P. Borja Rosales, Jacquelien M.A. Scherpen, Kenji Fujimoto