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Pure Mathematics 2025
基于Lyapunov理论的状态依赖延迟脉冲系统输入到状态稳定性研究
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Abstract:
本文研究了状态依赖延迟(State-Dependent Delay, SDD)脉冲系统的输入到状态稳定性(Input-to-Sate Stability, ISS)方面的特性，采用Lyapunov-Krasovskii函数与平均脉冲间隔分析，推导出了确保该系统ISS的必要条件。研究表明，稳定的SDD脉冲系统遭受不稳定脉冲扰动的情况下，系统依然能够保持ISS属性。另一方面，基于脉冲控制策略，我们构建了一套基于Lyapunov理论的充分条件，用以评估系统的ISS状态。研究表明，本质不稳定的SDD脉冲系统也可以保持ISS状态，达成预期性能。最终，给出两个数值案例验证理论结果的精确性和实用性。
In this paper, we examine the properties of state-dependent delay (SDD) impulsive systems in terms of input-to-state stability (ISS), and derive the necessary conditions to ensure ISS for this system, using the Lyapunov-Krasovskii function with mean impulsive interval analysis. It is demonstrated that the stable SDD impulsive system suffers from unstable impulse interference, the system is still able to maintain the ISS property. Conversely, we have developed a set of sufficient conditions, founded on Lyapunov theory, to evaluate the ISS state of the system based on the impulse control strategy. It has been demonstrated that the intrinsically unstable SDD impulsive system can also maintain the ISS state and attain the anticipated performance. To conclude, we have presented two numerical cases to substantiate the precision and practicality of the theoretical outcomes.
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