{
  "abstract": "Stability of switched linear systems under arbitrary switching is a fundamental problem in control theory, closely related to the joint spectral radius (JSR), which characterizes the worst-case growth rate of system trajectories. In this paper, we contribute to the path-complete approach for approximating the JSR. This framework constructs algebraic stability certificates using labeled directed graphs, known as path-complete graphs. These certificates can be computed via an associated optimization problem. We propose an iterative algorithm that refines path-complete graphs in an efficient and parsimonious manner. The algorithm relies on a graph-theoretic analysis of the optimality conditions of the underlying optimization problem. In particular, we derive a sufficient condition under which the exact JSR is attained by a given path-complete graph. When this condition is not satisfied, we identify bottleneck nodes by analyzing the graph induced by the active constraints. We then use this information to refine the path-complete graph via local graph lifting (node splitting), and repeat the procedure. Numerical experiments demonstrate the effectiveness and scalability of the proposed approach, outperforming state-of-the-art methods on all challenging instances tested.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.00637",
  "author_total": 2,
  "authors": [
    {
      "name": "Léa Ninite"
    },
    {
      "name": "Raphaël M. Jungers"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7c9m4qsnnx6zn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.00637",
  "fulltext_url": null,
  "id": "7c9m4qsnnx6zn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.00637",
  "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": "W7167065759",
  "pdf_url": "https://arxiv.org/pdf/2607.00637",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7c9m4qsnnx6zn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2607.00637",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.00637"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Iterative graph lifting for automatic design of path-complete stability certificates",
  "title_text": "Iterative graph lifting for automatic design of path-complete stability certificates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/7c9m4qsnnx6zn",
  "venue": "arXiv",
  "versions": []
}