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PreprintCC BY 4.0HAL

Refinement of the Leonov Function Framework for Global Boundedness of State-Periodic Systems

  • Marcel Fang
  • Denis Efimov
  • Mohammad Javad Mirzaei
  • Johannes Schiffer
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Abstract

Sufficient conditions for global boundedness of solutions of state-periodic systems are given. The results are grounded on the existence of a Leonov function. In contrast to previous works using a similar approach, our results are established by exploiting the invariance property of particular cells in the state space, rather than their attractivity. This novel approach substantially simplifies the requirements of Leonov functions for both fully and partially periodic systems. The effectiveness of the proposed conditions is illustrated on a heterogeneous network of Kuramoto oscillators and on a synchronous generator connected to an infinite bus.

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Cite

BibTeXRIS
BibTeX
@misc{fang2026refinement,
  title = {{Refinement of the Leonov Function Framework for Global Boundedness of State-Periodic Systems}},
  author = {Marcel Fang and Denis Efimov and Mohammad Javad Mirzaei and Johannes Schiffer},
  howpublished = {HAL},
  year = {2026},
  month = nov,
  url = {https://inria.hal.science/hal-05856522v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Refinement of the Leonov Function Framework for Global Boundedness of State-Periodic Systems
AU  - Marcel Fang
AU  - Denis Efimov
AU  - Mohammad Javad Mirzaei
AU  - Johannes Schiffer
PY  - 2026
DA  - 2026/11/09
PB  - HAL
UR  - https://inria.hal.science/hal-05856522v1
AB  - Sufficient conditions for global boundedness of solutions of state-periodic systems are given. The results are grounded on the existence of a Leonov function. In contrast to previous works using a similar approach, our results are established by exploiting the invariance property of particular cells in the state space, rather than their attractivity. This novel approach substantially simplifies the requirements of Leonov functions for both fully and partially periodic systems. The effectiveness of the proposed conditions is illustrated on a heterogeneous network of Kuramoto oscillators and on a synchronous generator connected to an infinite bus.
ER  -