Finite-time stability analysis and \\( H^\infty \\)-control for a class of nonlinear time-delay Hamiltonian systems

Authors

Renming Yang, Yuzhen Wang

Abstract

This paper investigates the finite-time stability (FTS) analysis and finite-time H ∞ control design for a class of nonlinear time-delay Hamiltonian systems, and proposes some delay-dependent results on both the FTS and finite-time control design. First, a criterion on the FTS is proposed for general time-delay nonlinear systems via the Razumikhin approach. Then, based on the criterion, some delay-independent and delay-dependent conditions on the FTS are derived for the nonlinear time-delay Hamiltonian systems by constructing a suitable Lyapunov function. Third, we use the obtained FTS results to investigate the finite-time H ∞ control problem, and present a control design procedure for a class of nonlinear time-delay port-controlled Hamiltonian systems by the energy-shaping approach. Study of two illustrative examples shows that the results obtained in this paper work very well in the FTS analysis and control design of some nonlinear time-delay Hamiltonian systems.

Keywords

energy shaping, finite-time \( H^\infty \)-control, finite-time stability, nonlinear time-delay hamiltonian system, razumikhin approach

Citation

• Journal: Automatica
• Year: 2013
• Volume: 49
• Issue: 2
• Pages: 390–401
• Publisher: Elsevier BV
• DOI: 10.1016/j.automatica.2012.11.034

BibTeX

@article{Yang_2013,
  title={{Finite-time stability analysis and
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                      <mml:msub>
                        <mml:mrow>
                          <mml:mi>H</mml:mi>
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                        <mml:mrow>
                          <mml:mi>∞</mml:mi>
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                    control for a class of nonlinear time-delay Hamiltonian systems},
  volume={49},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2012.11.034},
  number={2},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Yang, Renming and Wang, Yuzhen},
  year={2013},
  pages={390--401}
}

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