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<p>This paper studies the sliding mode control (SMC) problem for discrete Markov jump systems (MJSs) with actuator saturation. Firstly, a dynamic event-triggered mechanism (DETM) is designed between the system factory and the controller to effectively reduce the number of triggers while maintaining the desired control performance. Secondly, the sliding surface based on actuator saturation is designed. In order to eliminate the non-strict constraints and give the results of strict matrix inequalities, the sufficient conditions for the stochastic stability with <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="34_2025_3174_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(H_{\infty }\)</EquationSource> </InlineEquation> performance level <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="34_2025_3174_Article_IEq4.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma \)</EquationSource> </InlineEquation> of the sliding mode system are derived. Then, the sliding mode controller of the discrete MJSs is designed according to the designed sliding mode surface (SMS) and the arrival condition. Next, the maximum estimation of the domain of attraction (DOA) is obtained through the optimization process. Finally, the efficiency of the proposed approach is illustrated through two examples: one numerical and the other practical.</p>

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Dynamic Event-Triggered \(H_{\infty }\) Sliding Mode Control of Discrete-Time Markov Jump Systems with Actuator Saturation

  • 期刊论文

  • 发表日期：

    2025年6月9日

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  • Ziqiang Xu,
  • Junchao Ren

摘要

This paper studies the sliding mode control (SMC) problem for discrete Markov jump systems (MJSs) with actuator saturation. Firstly, a dynamic event-triggered mechanism (DETM) is designed between the system factory and the controller to effectively reduce the number of triggers while maintaining the desired control performance. Secondly, the sliding surface based on actuator saturation is designed. In order to eliminate the non-strict constraints and give the results of strict matrix inequalities, the sufficient conditions for the stochastic stability with \(H_{\infty }\) performance level \(\gamma \) of the sliding mode system are derived. Then, the sliding mode controller of the discrete MJSs is designed according to the designed sliding mode surface (SMS) and the arrival condition. Next, the maximum estimation of the domain of attraction (DOA) is obtained through the optimization process. Finally, the efficiency of the proposed approach is illustrated through two examples: one numerical and the other practical.