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PreprintCC BY 4.0arXiv

Truncated ℋ2 Optimal Model Order Reduction for Bilinear Quadratic Output Systems

  • Heike Faßbender
  • Serkan Gugercin
  • Till Peters
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Abstract

We develop an ℋ2 model reduction framework for polynomial bilinear systems with quadratic outputs. We define the associated ℋ2 norm and show its consistency with the established norm in the original (non-polynomial) BQO case. We derive first-order necessary conditions for ℋ2 optimal model reduction of these polynomial systems and use them to construct an efficient iterative algorithm for computing reduced BQO models that approximately satisfy these conditions. Numerical results on two examples demonstrate the accuracy and effectiveness of the proposed reduction approach.

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Cite

BibTeXRIS
BibTeX
@misc{faßbender2026truncated,
  title = {{Truncated $\mathcalH_2$ Optimal Model Order Reduction for Bilinear Quadratic Output Systems}},
  author = {Heike Faßbender and Serkan Gugercin and Till Peters},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37387},
  eprint = {2610.37387},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37387},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Truncated ℋ_2 Optimal Model Order Reduction for Bilinear Quadratic Output Systems
AU  - Heike Faßbender
AU  - Serkan Gugercin
AU  - Till Peters
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37387
UR  - https://arxiv.org/abs/2610.37387
AB  - We develop an ℋ_2 model reduction framework for polynomial bilinear systems with quadratic outputs. We define the associated ℋ_2 norm and show its consistency with the established norm in the original (non-polynomial) BQO case. We derive first-order necessary conditions for ℋ_2 optimal model reduction of these polynomial systems and use them to construct an efficient iterative algorithm for computing reduced BQO models that approximately satisfy these conditions. Numerical results on two examples demonstrate the accuracy and effectiveness of the proposed reduction approach.
ER  -