{
  "abstract": "Transfer functions of Partial Differential Equations (PDEs) are irrational and difficult to obtain. Unlike for rational transfer functions, only a few methods are available for the control and analysis of irrational transfer functions. Thus, for robust analysis and control of PDEs, we need to use a rational approximation of the transfer function, preferably with provable $H_\\infty$ error bounds. In this paper, we extend Krylov subspace model reduction to infinite-dimensional systems modeled by Partial Integral Equations (PIEs) -- an equivalent representation of PDEs. First, we propose a state transformation of the PIE system that allows us to compute a controllability matrix. Then, to obtain a rational approximation, we project the PIE states onto the vector space spanned by the truncated controllability matrix. Next, we show that sufficient conditions for exponential stability and well-posedness of the PIE system guarantee the exponential stability of the reduced-order system and provide constructive finite-frequency $H_\\infty$ error bounds. Finally, we provide four illustrative numerical examples to demonstrate the performance of the proposed method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08497",
  "author_total": 2,
  "authors": [
    {
      "name": "Aleksandr Talitckii"
    },
    {
      "name": "Matthew M. Peet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/489gcgm4r7yss.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08497",
  "fulltext_url": null,
  "id": "489gcgm4r7yss",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08497",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7221064457",
  "pdf_url": "https://arxiv.org/pdf/2610.08497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/489gcgm4r7yss.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08497"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stable Rational Approximation of PDE Transfer Functions with $H_\\infty$ Error Bounds",
  "title_text": "Stable Rational Approximation of PDE Transfer Functions with H_∞ Error Bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/489gcgm4r7yss",
  "venue": "arXiv",
  "versions": []
}