{
  "abstract": "We show that unless P = NP, there cannot be a polynomial-time (or even pseudo-polynomial-time) algorithm for output feedback stabilization of a linear dynamical system with a linear controller. This settles one of the best-known open problems in control theory. The result holds in both continuous and discrete time. We also present a family of stabilizable linear dynamical systems for which no polynomial-time algorithm can write down a stabilizing controller in its standard representation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20636",
  "author_total": 4,
  "authors": [
    {
      "name": "Amir Ali Ahmadi"
    },
    {
      "name": "Abraar Chaudhry"
    },
    {
      "name": "Ijay Narang"
    },
    {
      "name": "Yukai Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2asc9ee0hk7km.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20636",
  "fulltext_url": null,
  "id": "2asc9ee0hk7km",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20636",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "cs.CC"
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      "arxiv",
      "eess.SY"
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      "arxiv",
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      "openalex",
      "1703|Complexity and Algorithms in Graphs"
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  "openalex": "W7213579085",
  "pdf_url": "https://arxiv.org/pdf/2609.20636",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2asc9ee0hk7km.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.20636",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20636"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Complexity of Output Feedback Stabilization",
  "title_text": "Complexity of Output Feedback Stabilization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/2asc9ee0hk7km",
  "venue": "arXiv",
  "versions": []
}