Exponential stability preserving of two spatially discretized port-Hamiltonian systems

Authors

Fu Zheng, Hongjian Yin, Zhongjie Han, Bao-Zhu Guo

Abstract

For an ideal transmission line described by the telegrapher’s equations, a mixed finite element method-an extension of widely used spatially discretized approach-has been introduced. This numerical approximation approach maintains both the Dirac structure and passivity, guaranteeing that the spatially discretized system preserves its port-Hamiltonian characteristics. In this paper, we employ this method to spatially discretize two infinite-dimensional port-Hamiltonian systems characterized by variable coefficients and boundary controls. Subsequently, we explore the preservation of exponential stability in the resulting semi-discretized systems, establishing their uniform exponential stability concerning discretization parameters. Through frequency domain analysis, uniform exponential stability is demonstrated for both semi-discretized models. Finally, numerical simulations confirm the efficacy of this semi-discrete approach.

Keywords

Port-Hamiltonian system; Exponential stabilization; Mixed finite element; Semi-discretization; Frequency domain

Citation

• Journal: Journal of Differential Equations
• Year: 2026
• Volume: 453
• Issue:
• Pages: 113865
• Publisher: Elsevier BV
• DOI: 10.1016/j.jde.2025.113865

BibTeX

@article{Zheng_2026,
  title={{Exponential stability preserving of two spatially discretized port-Hamiltonian systems}},
  volume={453},
  ISSN={0022-0396},
  DOI={10.1016/j.jde.2025.113865},
  journal={Journal of Differential Equations},
  publisher={Elsevier BV},
  author={Zheng, Fu and Yin, Hongjian and Han, Zhongjie and Guo, Bao-Zhu},
  year={2026},
  pages={113865}
}

Download the bib file

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