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<p>This study investigates the reachable set control issue for singular Markov jump systems (SMJSs) with time-varying delays. With the aim of reducing unnecessary communication in networked environments, an event-triggered mechanism (ETM) is introduced. However, the incorporation of the ETM induces mismatches in the algebraic equations at sampling instants. To tackle this challenge, a hybrid impulsive control strategy, comprising a feedback controller and an impulsive controller, is developed to dynamically adjust the system state at each triggering instant. Based on this framework, a Lyapunov functional is constructed. Sufficient conditions are derived by combining linear matrix inequality techniques with the free-weighting matrix method to ensure the boundedness of the system states. The corresponding controller gains are consequently obtained. Moreover, it is rigorously proven that the proposed ETM does not exhibit Zeno behavior. Finally, a numerical example and a circuit model are provided to verify the effectiveness of the method.</p>

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Reachable Set Synthesis of Singular Markov Jump Systems with Time-Varying Delay via Event-Triggered Hybrid Impulsive Control

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Xinyu Zhang,
  • Liang Zhang,
  • Ning Liu,
  • Ning Zhao,
  • Yongchao Liu

摘要

This study investigates the reachable set control issue for singular Markov jump systems (SMJSs) with time-varying delays. With the aim of reducing unnecessary communication in networked environments, an event-triggered mechanism (ETM) is introduced. However, the incorporation of the ETM induces mismatches in the algebraic equations at sampling instants. To tackle this challenge, a hybrid impulsive control strategy, comprising a feedback controller and an impulsive controller, is developed to dynamically adjust the system state at each triggering instant. Based on this framework, a Lyapunov functional is constructed. Sufficient conditions are derived by combining linear matrix inequality techniques with the free-weighting matrix method to ensure the boundedness of the system states. The corresponding controller gains are consequently obtained. Moreover, it is rigorously proven that the proposed ETM does not exhibit Zeno behavior. Finally, a numerical example and a circuit model are provided to verify the effectiveness of the method.