{
  "abstract": "Given an unstable linear scalar differential equation $dx(t)=θx(t)dt$, $θ>0$, we show that it can be almost surely exponentially stabilized by a discrete-time feedback control driven by a general $α$-stable process. More precisely, consider the stochastically controlled system $dx(t)=θx(t)dt+bx(\\lfloor t/τ\\rfloorτ)dZ(t)$, where $Z(t)$ is a general $α$-stable process with $α\\in(1,2)$, and $\\lfloor t/τ\\rfloor$ denotes the integer part of $t/τ$. Unlike the extensively studied driven Brownian-driven case, the $α$-stable process has no finite second moment, so high-order moment methods are no longer applicable. By using fractional moments, characteristic functions, and moment inequalities for $α$-stable stochastic integrals, we prove that the stochastically controlled system is almost surely exponentially stable provided that the inequality $|bσ|^α\\left(1-β\\operatorname{sgn}(b)\\tan^2\\frac{πα}{2}\\right)>(θ+bμ) \\frac{-1}{Γ(α)\\cos\\frac{απ}{2}}$ holds, and that $τ>0$ is sufficiently small.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04340",
  "author_total": 1,
  "authors": [
    {
      "name": "Xuekang Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5r4q9pgx3qsfk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04340",
  "fulltext_url": null,
  "id": "5r4q9pgx3qsfk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04340",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04340",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5r4q9pgx3qsfk.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04340",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04340"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Almost sure exponential stabilization of linear stochastic systems driven by a general $α$-stable process via discrete-time state feedback",
  "title_text": "Almost sure exponential stabilization of linear stochastic systems driven by a general α-stable process via discrete-time state feedback",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/5r4q9pgx3qsfk",
  "venue": "arXiv",
  "versions": []
}