{
  "abstract": "The paper introduces a successive backstepping observer design for strictly feedforward parabolic PDE-ODE systems, in which the coupling structure determines the order of error stabilization and the corresponding transformations. First, a transformation based on a virtual measurement stabilizes the ODE observer error subsystem, which is most distal from the measurement, while decoupling it from the PDE error state. Second, a Volterra integral transformation is employed to stabilize the PDE error subsystem and to map the overall error dynamics into a cascade of exponentially stable ODE and PDE subsystems. The design is shown to be dual to a recently proposed multi-step state feedback design for parabolic PDE-ODE systems in strict feedback form, thus explaining the structure of the presented observer design.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29693",
  "author_total": 1,
  "authors": [
    {
      "name": "Nicole Gehring"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0v6gcg770gzh1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29693",
  "fulltext_url": null,
  "id": "0v6gcg770gzh1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29693",
  "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": [
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      "cs.SY"
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      "arxiv",
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      "2207|Stability and Controllability of Differential Equations"
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  "openalex": "W7204940989",
  "pdf_url": "https://arxiv.org/pdf/2608.29693",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0v6gcg770gzh1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29693",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29693"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Successive design of backstepping observers for parabolic PDE-ODE systems and its duality to state feedback stabilization",
  "title_text": "Successive design of backstepping observers for parabolic PDE-ODE systems and its duality to state feedback stabilization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/0v6gcg770gzh1",
  "venue": "arXiv",
  "versions": []
}