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<p>In this paper, we introduce a new notion of stability for nonlinear time-varying systems called <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2931_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(h^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>h</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-stability which represents a generalization of existing works in the literature. The main purpose of this new notion is to investigate the global uniform <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2931_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(h^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>h</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-stability of a class of time-varying systems using Lyapunov method that involves indefinite derivatives. Moreover, we provide illustrative examples to showcase the application and effectiveness of our proposed approach.</p>

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Global Uniform \(h^*\)-Stability of Time-Varying Perturbed Systems

  • 期刊论文

  • 发表日期：

    2025年8月7日

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  • Sahbi Boughattas,
  • Nizar Hadj Taieb

摘要

In this paper, we introduce a new notion of stability for nonlinear time-varying systems called \(h^*\) h ∗ -stability which represents a generalization of existing works in the literature. The main purpose of this new notion is to investigate the global uniform \(h^*\) h ∗ -stability of a class of time-varying systems using Lyapunov method that involves indefinite derivatives. Moreover, we provide illustrative examples to showcase the application and effectiveness of our proposed approach.