{
  "abstract": "This paper addresses the stabilization of switched affine systems under dwell-time constraints around a desired operating point that is not a common equilibrium of the subsystems. Since asymptotic stabilization is generally unattainable in this setting, the objective is to ensure that trajectories converge to and remain within a prescribed region containing the desired operating point. The main contribution is the development of Lyapunov-based tools that accommodate target regions more general than those induced by quadratic Lyapunov functions. In particular, we establish a constructive Lyapunov characterization for a broad family of weighted $p$-norm functions, which generalizes the classical quadratic Lyapunov equivalence and underpins the proposed hybrid-control and dwell-time developments. Focusing on the case in which the desired region is a polytope, and building on existing Lyapunov-based methods, we develop a constructive two-step method that starts from a polytopic Lyapunov certificate for the average system and yields a smooth weighted $p$-norm Lyapunov function for all sufficiently large $p$. We prove that this extension guarantees practical asymptotic stability of the desired operating point and yields a Lyapunov-certified invariant region under minimum dwell-time switching. Numerical examples illustrate the effectiveness of the proposed method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37840",
  "author_total": 4,
  "authors": [
    {
      "name": "Felipe Cinto"
    },
    {
      "name": "Alexis J. Vallarella"
    },
    {
      "name": "Hernan Haimovich"
    },
    {
      "name": "Paulo C. Pellanda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1tnpmw8pn3e3c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37840",
  "fulltext_url": null,
  "id": "1tnpmw8pn3e3c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37840",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Control of Uncertain Systems"
    ]
  ],
  "openalex": "W7214917548",
  "pdf_url": "https://arxiv.org/pdf/2609.37840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1tnpmw8pn3e3c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Practical Stabilization of Switched Affine Systems under Dwell Time: From Polytopic to p-Norm Lyapunov Functions",
  "title_text": "Practical Stabilization of Switched Affine Systems under Dwell Time: From Polytopic to p-Norm Lyapunov Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/1tnpmw8pn3e3c",
  "venue": "arXiv",
  "versions": []
}