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<p>In this paper, finite-time contractive (FTC) stabilization and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {H}_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> control are discussed for switched nonlinear systems (SNSs) under the switched nonlinear port-controlled Hamiltonian system (SNPHS) framework, where several transformation relationships are introduced to link SNSs to SNPHSs. To ensure finite-time stability (FTS) of the closed-loop SNPHS and further achieve finite-time contractive stability (FTCS), we develop a switching state-feedback (SSF) controller together with two trade-off-based mode-dependent average dwell-time (MDADT) switching schemes. FTC stabilization conditions are then derived for both SNPHSs and the associated SNSs. Moreover, to attain <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal {H}_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> FTCS performance, we introduce the maximum ratio of the activation time of unstable modes and, together with the proposed trade-off-based MDADT schemes, sufficient conditions on <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal {H}_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> FTCS control are also established for both SNPHSs and the associated SNSs via the SSF control design. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed results.</p>

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Finite-time contractive stabilization and \(\mathcal {H}_\infty \) control for switched nonlinear systems with trade-off-based MDADT switching

  • 期刊论文

  • 发表日期：

    2026年5月12日

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  • Yu-Han Liu,
  • Zi-Ming Wang,
  • Xudong Zhao

摘要

In this paper, finite-time contractive (FTC) stabilization and \(\mathcal {H}_\infty \) H ∞ control are discussed for switched nonlinear systems (SNSs) under the switched nonlinear port-controlled Hamiltonian system (SNPHS) framework, where several transformation relationships are introduced to link SNSs to SNPHSs. To ensure finite-time stability (FTS) of the closed-loop SNPHS and further achieve finite-time contractive stability (FTCS), we develop a switching state-feedback (SSF) controller together with two trade-off-based mode-dependent average dwell-time (MDADT) switching schemes. FTC stabilization conditions are then derived for both SNPHSs and the associated SNSs. Moreover, to attain \(\mathcal {H}_\infty \) H ∞ FTCS performance, we introduce the maximum ratio of the activation time of unstable modes and, together with the proposed trade-off-based MDADT schemes, sufficient conditions on \(\mathcal {H}_\infty \) H ∞ FTCS control are also established for both SNPHSs and the associated SNSs via the SSF control design. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed results.