{
  "abstract": "Approximating the maximum retained energy fraction in globally asymptotically stable quadratic systems of growing dimension is NP-hard at every fixed positive additive error below $1/2$, even when strict quartic Lyapunov functions and strictness proofs are constructed in polynomial time and included in the input. Polynomial-factor approximation is also NP-hard for the least dissipated fraction, energy-halving time and structured coefficient distance to loss of asymptotic stability. For a partially damped family, minimum unit-sphere coupling norm equals that distance, with two-sided inverse-square halving-time bounds at distances in $(0,1/2]$ and explicit coefficient factors. Additive hardness persists under structured coefficient perturbations and direct damping, even with global exponential stability, a strict quadratic Lyapunov function and a Hurwitz Jacobian.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29512",
  "author_total": 1,
  "authors": [
    {
      "name": "Subhransu S. Bhattacharjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82qfwsvp0xhhq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29512",
  "fulltext_url": null,
  "id": "82qfwsvp0xhhq",
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  "landing_url": "https://arxiv.org/abs/2610.29512",
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  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "2207|Control and Stability of Dynamical Systems"
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  "openalex": "W7223226939",
  "pdf_url": "https://arxiv.org/pdf/2610.29512",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82qfwsvp0xhhq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.29512",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29512"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Dissipation Bounds and Hardness in Globally Asymptotically Stable Quadratic Systems",
  "title_text": "Dissipation Bounds and Hardness in Globally Asymptotically Stable Quadratic Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/82qfwsvp0xhhq",
  "venue": "arXiv",
  "versions": []
}