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<p>Based on the Roesser model, this paper explores the asynchronous control problem of 2-D Markov jump systems. Targeting the circumstance whereby the system mode is not precisely obtainable in real-world applications, the hidden Markov model is adopted to observe the system mode. In order to deal with the performance degradation caused by saturation constraint and the difficulty of obtaining complete probability information in practice, this paper also considers the unknown transition probability and observation probability while studying actuator saturation. Through the creation of a Lyapunov function, some sufficient conditions are obtained for the closed-loop system to satisfy asymptotic mean square stability and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11642_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> performance indicators under partial probability information. In light of these conditions, the appropriate controller gains can be obtained, while the attraction domain is estimated via an optimization algorithm. Lastly, numerical and thermal process examples are used to confirm the efficacy of the constructed asynchronous controller.</p>

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Asynchronous control of 2-D Markov jump systems subject to actuator saturation and partially known probabilities

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Wenhao Zhang,
  • Lei Su,
  • Feng Li,
  • Tian Fang

摘要

Based on the Roesser model, this paper explores the asynchronous control problem of 2-D Markov jump systems. Targeting the circumstance whereby the system mode is not precisely obtainable in real-world applications, the hidden Markov model is adopted to observe the system mode. In order to deal with the performance degradation caused by saturation constraint and the difficulty of obtaining complete probability information in practice, this paper also considers the unknown transition probability and observation probability while studying actuator saturation. Through the creation of a Lyapunov function, some sufficient conditions are obtained for the closed-loop system to satisfy asymptotic mean square stability and \(H_{\infty }\) H ∞ performance indicators under partial probability information. In light of these conditions, the appropriate controller gains can be obtained, while the attraction domain is estimated via an optimization algorithm. Lastly, numerical and thermal process examples are used to confirm the efficacy of the constructed asynchronous controller.