{
  "abstract": "We study fixed-time input-to-state stability (FxT-ISS) for discrete-time systems subject to exogenous inputs. We introduce Lyapunov-based sufficient conditions for FxT- ISS based on a class of dissipation functions with a fixed-time extinction property, which encompasses commonly used two- power constructions while allowing substantially more general decay mechanisms. Building on this framework, we establish a small-gain theorem for interconnected FxT-ISS systems in the presence of disturbances. The results are illustrated through several examples, including perturbed optimization algorithms and a discrete-time feedback-optimization architecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00657",
  "author_total": 2,
  "authors": [
    {
      "name": "Sumadhu Rubaiyat"
    },
    {
      "name": "Jorge I. Poveda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5p8xd4cxn52nx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00657",
  "fulltext_url": null,
  "id": "5p8xd4cxn52nx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00657",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Control of Uncertain Systems"
    ]
  ],
  "openalex": "W7216129127",
  "pdf_url": "https://arxiv.org/pdf/2610.00657",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5p8xd4cxn52nx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00657",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00657"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Fixed-Time ISS for Interconnected Discrete-Time Systems, Part I: Extinction-Based Lyapunov Functions",
  "title_text": "Fixed-Time ISS for Interconnected Discrete-Time Systems, Part I: Extinction-Based Lyapunov Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/5p8xd4cxn52nx",
  "venue": "arXiv",
  "versions": []
}