A Lyapunov Approach for the Exponential Stability of a Damped Timoshenko Beam

Authors

Andrea Mattioni, Yongxin Wu, Yann Le Gorrec

Abstract

In this technical note, we consider the stability properties of a viscously damped Timoshenko beam equations with spatially varying parameters. With the help of the port-Hamiltonian framework, we first prove the existence of solutions and show, by the use of an appropriate Lyapunov function, that the system is exponentially stable and has an explicit decay rate. The explicit exponential bound is computed for an illustrative example for which we provide some numerical simulations.

Citation

• Journal: IEEE Transactions on Automatic Control
• Year: 2023
• Volume: 68
• Issue: 12
• Pages: 8287–8292
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tac.2023.3297499

BibTeX

@article{Mattioni_2023,
  title={{A Lyapunov Approach for the Exponential Stability of a Damped Timoshenko Beam}},
  volume={68},
  ISSN={2334-3303},
  DOI={10.1109/tac.2023.3297499},
  number={12},
  journal={IEEE Transactions on Automatic Control},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Mattioni, Andrea and Wu, Yongxin and Le Gorrec, Yann},
  year={2023},
  pages={8287--8292}
}

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References

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