一类新的二重积分不等式在时滞系统中的应用
A Novel Double Integral Inequalities Applied to Time-Delay Systems
DOI: 10.12677/PM.2021.118172, PDF,    国家自然科学基金支持
作者: 叶永佳, 熊良林, 张海洋：云南民族大学数学与计算机科学学院，云南 昆明
关键词: 时变时滞；增广的李雅普诺夫泛函；自由矩阵不等式；时滞分割；Time-Varying Delay； Augmented Lyapunov Functional； Free-Base-Matrix Inequality； Delay Partition
摘要: 本文主要研究一类新的二重积分不等式并用于时滞系统的稳定性分析。首先，通过引入零等式得到新的二重积分不等式。然后，利用增广向量构造李雅普诺夫泛函(LKF)，再通过不等式对泛函导数中的积分项进行处理，得到保守性更低的稳定性条件。接着用更加宽松的二次函数负决定引理得到新的稳定条件。最后，通过一个数值例子验证所得结果的有效性和优越性。
Abstract: This article is concerned with a novel double integral inequalities applied to time-delay systems. Firstly, two zero-value equations have been introduced to estimate the upper bound of double in-tegral inequality. Secondly, augmented vectors are used to construct Lyapunov function, and the inequality is utilized to estimate the derivative of functional, and then relax quadratic function negative-determination lemma is used to obtain stability criterion. Finally, examples are given to show the effectiveness of the obtained result.
文章引用：叶永佳, 熊良林, 张海洋. 一类新的二重积分不等式在时滞系统中的应用[J]. 理论数学, 2021, 11(8): 1535-1545. https://doi.org/10.12677/PM.2021.118172

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