{
  "abstract": "Recently, dynamic state feedback controllers that are based on dynamic extensions have been presented for heterodirectional hyperbolic systems. In this paper, a similar concept for the control of coupled diffusion-reaction systems is suggested. The introduction of a specific controller dynamics leads to homogenized diffusion coefficients for the extended system. Then, a backstepping-based static state feedback for the dynamically extended system is designed, which, overall, results in a dynamic state feedback. Such a design allows stabilizing a more general class of parabolic systems as well as assigning arbitrary closed-loop dynamics. This can be used, e.g., to achieve a decoupled input-output behavior, which is, in general, not possible with a static state feedback. A simulation example illustrates the results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17293",
  "author_total": 4,
  "authors": [
    {
      "name": "Nicole Gehring"
    },
    {
      "name": "Benedikt Schwämmle"
    },
    {
      "name": "Abdurrahman Irscheid"
    },
    {
      "name": "Joachim Deutscher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8e8689096ee7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17293",
  "fulltext_url": null,
  "id": "d8e8689096ee7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17293",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
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      "arxiv",
      "eess.SY"
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    [
      "arxiv",
      "math.OC"
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      "openalex",
      "2207|Stability and Controllability of Differential Equations"
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  "openalex": "W7213408191",
  "pdf_url": "https://arxiv.org/pdf/2609.17293",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8e8689096ee7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17293",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17293"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Backstepping Design of Dynamic State Feedback Controllers for Parabolic Systems",
  "title_text": "Backstepping Design of Dynamic State Feedback Controllers for Parabolic Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/d8e8689096ee7",
  "venue": "arXiv",
  "versions": []
}