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Pure Mathematics 2024
基于三次函数不等式的时变时滞系统稳定性分析
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Abstract:
时滞系统的稳定性分析一直是学术研究的焦点。本文采用Lyapunov-Krasovskii泛函(LKF)方法，对时变时滞系统的稳定性进行了深入研究，并提出了一个互凸三次矩阵不等式。首先，利用辅助函数积分不等式和互凸三次矩阵不等式，对LKF导数中的积分项进行了有效估计。随后，基于三次函数负定方法，以线性矩阵不等式(LMI)的形式给出了时变时滞系统渐近稳定的稳定性准则，以确保系统的稳定性。最后，通过数值例子，验证了所提出方法的可行性和优越性。
The stability analysis of time-delay systems has always been a focus of academic research. This article adopts the Lyapunov Krasovskii functional (LKF) method to conduct in-depth research on the stability of time-varying time-delay systems, and proposes a mutually convex cubic matrix inequality. Firstly, the integral terms in the LKF derivative are effectively estimated using the auxiliary function integral inequality and the convex cubic matrix inequality. Subsequently, based on the negative definite method of cubic functions, a stability criterion for asymptotic stability of time-varying time-delay systems is presented in the form of linear matrix inequality (LMI) to ensure the stability of the system. Finally, the feasibility and superiority of the proposed method are verified through numerical examples.
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