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<p>Recently, many research works have been devoted to adapt fundamental concepts of control theory to conformable fractional systems. In this direction, the paper addresses the questions of the stability and the stabilizability of these systems in an infinite-dimensional state space setting. First, we state a sufficient condition for the exponential stability of a conformable <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2024_1558_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-semigroup of order <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2024_1558_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation> on a Banach space. Then, we prove a useful result related to conformable stability of semilinear systems. Finally, we study the conformable stabilizability of the controlled semilinear systems. An example is provided to illustrate the effectiveness of our theoretical result related to the stability of semilinear systems.</p>

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Stability and stabilizability for infinite-dimensional conformable semilinear systems

  • 期刊论文

  • 发表日期：

    2025年1月15日

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  • Toufik Ennouari,
  • Bouchra Abouzaid,
  • Mohammed Elarbi Achhab

摘要

Recently, many research works have been devoted to adapt fundamental concepts of control theory to conformable fractional systems. In this direction, the paper addresses the questions of the stability and the stabilizability of these systems in an infinite-dimensional state space setting. First, we state a sufficient condition for the exponential stability of a conformable \(C_0\) C 0 -semigroup of order \(\delta \) δ on a Banach space. Then, we prove a useful result related to conformable stability of semilinear systems. Finally, we study the conformable stabilizability of the controlled semilinear systems. An example is provided to illustrate the effectiveness of our theoretical result related to the stability of semilinear systems.