Interpolatory \\( \boldsymbol {[[:space:]]{\mathcal {H}[[:space:]]}_{2}[[:space:]]} \\)-Optimality Conditions for Structured Linear Time-Invariant Systems

Authors

Petar Mlinarić, Peter Benner, Serkan Gugercin

Abstract

. Interpolatory necessary optimality conditions for [Formula: see text]-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on [Formula: see text]-optimal reduced-order modeling of stationary parametric problems, in this paper, we develop and investigate optimality conditions for [Formula: see text]-optimal reduced-order modeling of structured LTI systems, in particular, for second-order, port-Hamiltonian, and time-delay systems. Under certain diagonalizability assumptions, we show that across all these different structured settings, bitangential Hermite interpolation is the common form for optimality, thus proving a unifying optimality framework for structured reduced-order modeling.

Citation

• Journal: SIAM Journal on Numerical Analysis
• Year: 2025
• Volume: 63
• Issue: 2
• Pages: 949–975
• Publisher: Society for Industrial & Applied Mathematics (SIAM)
• DOI: 10.1137/23m1610033

BibTeX

@article{Mlinari__2025,
  title={{Interpolatory \(\boldsymbol {{\mathcal {H}}_{2}}\)-Optimality Conditions for Structured Linear Time-Invariant Systems}},
  volume={63},
  ISSN={1095-7170},
  DOI={10.1137/23m1610033},
  number={2},
  journal={SIAM Journal on Numerical Analysis},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Mlinarić, Petar and Benner, Peter and Gugercin, Serkan},
  year={2025},
  pages={949--975}
}

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