Extended Balancing of Continuous LTI Systems: A Structure-Preserving Approach

Authors

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

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.

Citation

• Journal: IEEE Transactions on Automatic Control
• Year: 2023
• Volume: 68
• Issue: 1
• Pages: 257–271
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tac.2021.3138645

BibTeX

@article{Borja_2023,
  title={{Extended Balancing of Continuous LTI Systems: A Structure-Preserving Approach}},
  volume={68},
  ISSN={2334-3303},
  DOI={10.1109/tac.2021.3138645},
  number={1},
  journal={IEEE Transactions on Automatic Control},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Borja, Pablo and Scherpen, Jacquelien M. A. and Fujimoto, Kenji},
  year={2023},
  pages={257--271}
}

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