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<p>This manuscript aims to fill the gap in the bounded real lemma and robust <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3271_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> control condition for fractional-order systems with distributed delay (FOSDDs). At first, two order-dependent and delay-dependent bounded real lemmas for FOSDDs are proposed. Then, a robust <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3271_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> control condition in form of linear matrix inequalities (LMIs) for the uncertain FOSDDs with norm-bounded uncertainties is obtained on the ground of the proposed bounded real lemmas. At last, several numerical examples are put forward to manifest the effectiveness and advantage of the obtained results.</p>

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The robust \(H_{\infty }\) control of fractional-order systems with distributed delay

  • 期刊论文

  • 发表日期：

    2025年6月6日

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  • Yi-Nan Chen,
  • Jun-Guo Lu,
  • Zhen Zhu

摘要

This manuscript aims to fill the gap in the bounded real lemma and robust \(H_{\infty }\) H ∞ control condition for fractional-order systems with distributed delay (FOSDDs). At first, two order-dependent and delay-dependent bounded real lemmas for FOSDDs are proposed. Then, a robust \(H_{\infty }\) H ∞ control condition in form of linear matrix inequalities (LMIs) for the uncertain FOSDDs with norm-bounded uncertainties is obtained on the ground of the proposed bounded real lemmas. At last, several numerical examples are put forward to manifest the effectiveness and advantage of the obtained results.