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<p>A Gronwall-type estimate for a class of nonlinear nonhomogeneous integral inequalities is given. By using the new inequality, a sufficient condition for finite-time stability of a nonlinear perturbed fractional-order system with time-varying delays is obtained, which corrects the results of finite-time stability caused by improper use of Gronwall inequality in relevant papers. This condition is applied to analyze the finite-time stability of Newcastle robot motion and fractional-order time delay neural networks. Finally, the obtained result is verified through numerical calculations.</p>

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Finite-time stability of delayed fractional-order system with nonlinear control

  • 期刊论文

  • 发表日期：

    2025年1月18日

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  • Xiangyu Xu,
  • Xindian Li,
  • Renwu Zhang,
  • Tiejun Zhou

摘要

A Gronwall-type estimate for a class of nonlinear nonhomogeneous integral inequalities is given. By using the new inequality, a sufficient condition for finite-time stability of a nonlinear perturbed fractional-order system with time-varying delays is obtained, which corrects the results of finite-time stability caused by improper use of Gronwall inequality in relevant papers. This condition is applied to analyze the finite-time stability of Newcastle robot motion and fractional-order time delay neural networks. Finally, the obtained result is verified through numerical calculations.