Stabilisation and \(\mathcal{H}_{\infty}\) control for switched port-controlled Hamiltonian systems with unstable modes and actuator saturation

Authors

Zi-Ming Wang, Airong Wei, Xudong Zhao, Jinge Yang, Guangdeng Zong

Abstract

In this paper, the problems of stabilisation and control are addressed for switched port-controlled Hamiltonian (SPCH) systems with unstable modes and actuator saturation (AS) via energy-based multiple Lyapunov functions methods. Firstly, by a switching state feedback controller with truncation-inequality techniques, the considered system is transformed into an unforced SPCH system with asymptotically stable, stable and unstable modes. Then, by developing an alternative switching law with slow/fast mode-dependent average dwell time (MDADT) switching scheme, new sufficient conditions are obtained for stabilisation of the SPCH system. Secondly, by designing a new switching feedback controller, revealing the characteristics of alternative switching signals and defining an indicative function, a new criterion for control of the SPCH systems with unstable modes and AS is achieved via the slow/fast MDADT switching scheme. Moreover, based on the obtained results and the indicative function, control conditions for the corresponding SPCH system are also derived under a slow MDADT switching scheme and a traditional average dwell time scheme, respectively. Finally, some numerical examples are given to verify the effectiveness of the proposed methods.

Citation

• Journal: International Journal of Systems Science
• Year: 2020
• Volume: 51
• Issue: 1
• Pages: 1–19
• Publisher: Informa UK Limited
• DOI: 10.1080/00207721.2019.1690071

BibTeX

@article{Wang_2019,
  title={{Stabilisation and ℋ∞control for switched port-controlled Hamiltonian systems with unstable modes and actuator saturation}},
  volume={51},
  ISSN={1464-5319},
  DOI={10.1080/00207721.2019.1690071},
  number={1},
  journal={International Journal of Systems Science},
  publisher={Informa UK Limited},
  author={Wang, Zi-Ming and Wei, Airong and Zhao, Xudong and Yang, Jinge and Zong, Guangdeng},
  year={2019},
  pages={1--19}
}

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