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<p>To solve the problem of fixed-time stabilization of <i>p</i>-normal nonlinear systems with dynamic uncertainty, we first obtain three important properties of fixed-time input-to-state stability (FxT-ISS) and FxT-ISS Lyapunov function. Then, by characterizing dynamic uncertainty with FxT-ISS, fully extracting the characteristics of system nonlinearities and applying the adding a power integrator technique, a continuous state-feedback controller is designed. Based on some technical conditions related to dynamic uncertainty, a new fixed-time stability theorem and its corollary are proposed. It is proved that every solution starting from initial point is well-defined and the equilibrium point of the closed-loop system is fixed-time stable. Finally, practical and numerical simulation results illustrate the effectiveness of this scheme.</p>

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Fixed-time stabilization of uncertain p-normal nonlinear systems and its application to liquid-level system

  • 期刊论文

  • 发表日期：

    2025年4月30日

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  • Kemei Zhang,
  • You Wu,
  • Xue-Jun Xie

摘要

To solve the problem of fixed-time stabilization of p-normal nonlinear systems with dynamic uncertainty, we first obtain three important properties of fixed-time input-to-state stability (FxT-ISS) and FxT-ISS Lyapunov function. Then, by characterizing dynamic uncertainty with FxT-ISS, fully extracting the characteristics of system nonlinearities and applying the adding a power integrator technique, a continuous state-feedback controller is designed. Based on some technical conditions related to dynamic uncertainty, a new fixed-time stability theorem and its corollary are proposed. It is proved that every solution starting from initial point is well-defined and the equilibrium point of the closed-loop system is fixed-time stable. Finally, practical and numerical simulation results illustrate the effectiveness of this scheme.