{
  "abstract": "This paper proposes a novel composite boundary feedback control law that ensures input-to-state stability (ISS) for a coupled ODE-parabolic PDE system with time-varying coefficients in both subsystems. In controller design, we circumvent the need to directly solve coupled time-varying parabolic-hyperbolic kernel equations by employing an analytic pre-defined gain function and a time-varying Volterra kernel function to design the control law explicitly. In stability analysis, to address the simultaneous challenges of Dirichlet boundary disturbances and time-varying coefficients, we employ the square root of a time-varying positive definite matrix and a superlinear function to construct a nonquadratic Lyapunov function for the ODE and a generalized Lyapunov functional for the PDE, respectively, in the target system, thereby establishing the ISS in the $L^2$-norm of the closed-loop system. Numerical simulations are presented to illustrate the effectiveness of the proposed control scheme.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06599",
  "author_total": 4,
  "authors": [
    {
      "name": "Yongchun Bi"
    },
    {
      "name": "Jun Zheng"
    },
    {
      "name": "Guchuan Zhu"
    },
    {
      "name": "Jiye Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0g6t3pvx1e76f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06599",
  "fulltext_url": null,
  "id": "0g6t3pvx1e76f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06599",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7212015735",
  "pdf_url": "https://arxiv.org/pdf/2609.06599",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0g6t3pvx1e76f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06599",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06599"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Input-to-State Stabilization of a Coupled ODE-PDE System with Time-Varying Coefficients via Composite Boundary Control",
  "title_text": "Input-to-State Stabilization of a Coupled ODE-PDE System with Time-Varying Coefficients via Composite Boundary Control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/0g6t3pvx1e76f",
  "venue": "arXiv",
  "versions": []
}