{
  "abstract": "We propose an exact formulation to quantify the finite-horizon robustness of a Linear Quadratic Regulator (LQR) subject to norm-bounded Linear Time-Invariant (LTI) parametric uncertainties, using the Performance Estimation Problem (PEP) framework. Originally developed for optimization, this method allows us to reformulate the worst-case performance search as a rank-constrained Semidefinite Program (SDP). By applying operator interpolation, this formulation retains the sequence variables, allowing the worst-case to be explicitly reconstructed when a rank-one solution is found. This approach also opens new possibilities for the finite-horizon certification of broader system classes, such as data-driven models or nonlinear components. Using this framework, we observe that finite-horizon LTI perturbations do not simply follow asymptotic strategies. Instead, they align slowly decaying invariant manifolds with specific initial conditions to drive transient growth, causing a bifurcation in the worst-case behavior as the horizon length changes. Finally, we show numerically that our performance bounds sit between the upper bounds of Integral Quadratic Constraint (IQC) relaxations and a lower bound derived from a pseudospectral heuristic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29910",
  "author_total": 3,
  "authors": [
    {
      "name": "Anthony Couthures"
    },
    {
      "name": "Gianluca Bianchin"
    },
    {
      "name": "Julien M. Hendrickx"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/emadfssk7ndhv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29910",
  "fulltext_url": null,
  "id": "emadfssk7ndhv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29910",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Control of Uncertain Systems"
    ]
  ],
  "openalex": "W7223240819",
  "pdf_url": "https://arxiv.org/pdf/2610.29910",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/emadfssk7ndhv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29910",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29910"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Worst-Case Finite-Horizon Analysis of Perturbed LQR via Performance Estimation Problem",
  "title_text": "Worst-Case Finite-Horizon Analysis of Perturbed LQR via Performance Estimation Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/emadfssk7ndhv",
  "venue": "arXiv",
  "versions": []
}