Port-Hamiltonian Boundary Control Systems in Discrete-Time Modeling and Control Design

Authors

Alessandro Macchelli

Abstract

This article presents a design framework of discrete-time regulators for linear port-Hamiltonian boundary control systems. The contribution is twofold. At first, a discrete-time approximation of the plant dynamics originally described by a linear partial differential equation with boundary actuation is introduced. The discretization is performed in time only. Thus, the “distributed nature” of the state is maintained. Such a system inherits the passivity of the original one and is well-posed, i.e., the “next” state always exists. In the second part, instead, the control design problem is tackled. Initially, the characterization of discrete-time, linear controllers in the port-Hamiltonian form that render the closed-loop dynamics asymptotically stable is presented. Then, the control by energy-shaping and damping injection paradigm is extended to deal with this novel class of distributed-parameter systems. A numerical example illustrates the effectiveness of the proposed framework.

Citation

• Journal: IEEE Transactions on Automatic Control
• Year: 2026
• Volume: 71
• Issue: 2
• Pages: 722–736
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tac.2025.3593062

BibTeX

@article{Macchelli_2026,
  title={{Port-Hamiltonian Boundary Control Systems in Discrete-Time Modeling and Control Design}},
  volume={71},
  ISSN={2334-3303},
  DOI={10.1109/tac.2025.3593062},
  number={2},
  journal={IEEE Transactions on Automatic Control},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Macchelli, Alessandro},
  year={2026},
  pages={722--736}
}

Download the bib file

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