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<p>Based on an algebraic point of view and the realization theory developed by Y. Yamamoto, the present paper states a necessary and sufficient criterion, given in the frequency domain, for the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="498_2025_418_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^q\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>q</mi> </msup> </math></EquationSource> </InlineEquation> approximate controllability in finite time of linear difference delay equations with distributed delays. Furthermore, an upper bound for the minimal time of the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="498_2025_418_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^q\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>q</mi> </msup> </math></EquationSource> </InlineEquation> approximate controllability is obtained.</p>

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\(L^q\) approximate controllability frequency criterion for linear difference delay equations with distributed delays

  • 期刊论文

  • 发表日期：

    2025年5月23日

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  • Sébastien Fueyo

摘要

Based on an algebraic point of view and the realization theory developed by Y. Yamamoto, the present paper states a necessary and sufficient criterion, given in the frequency domain, for the \(L^q\) L q approximate controllability in finite time of linear difference delay equations with distributed delays. Furthermore, an upper bound for the minimal time of the \(L^q\) L q approximate controllability is obtained.