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<p>This paper investigates stabilization and destabilization by periodic intermittent control for hybrid systems with Ornstein-Uhlenbeck processes. We introduce the periodic intermittent control strategy and establish the stability criterion of hybrid systems with Ornstein-Uhlenbeck processes. These criteria elucidate the effects of the control period <i>T</i>, the noise intensity <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7929_Article_IEq1.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>, reversion rate <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7929_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>, and volatility intensity <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7929_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varpi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϖ</mi> </math></EquationSource> </InlineEquation> on the hybrid systems. Finally, the theoretical results are applied to a representative system with Ornstein-Uhlenbeck processes, and their validity is confirmed through the numerical simulations.</p>

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STABILIZATION AND DESTABILIZATION BY INTERMITTENT CONTROL FOR HYBRID SYSTEMS WITH ORNSTEIN-UHLENBECK PROCESSES

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Guixin Hu,
  • Manqing Yang

摘要

This paper investigates stabilization and destabilization by periodic intermittent control for hybrid systems with Ornstein-Uhlenbeck processes. We introduce the periodic intermittent control strategy and establish the stability criterion of hybrid systems with Ornstein-Uhlenbeck processes. These criteria elucidate the effects of the control period T, the noise intensity \(\delta \) δ , reversion rate \(\mu \) μ , and volatility intensity \(\varpi \) ϖ on the hybrid systems. Finally, the theoretical results are applied to a representative system with Ornstein-Uhlenbeck processes, and their validity is confirmed through the numerical simulations.