Abstract The Lyapunov function method is a powerful tool to stability analysis of functional differential equations. However, this method is not effectively applied for fractional differential equations with delay, since the constructing Lyapunov-Krasovskii function and calculating its fractional derivative are still difficult. In this paper, to overcome this difficulty we propose an analytical approach, which is based on the Laplace transform and “inf-sup” method, to study finite-time stability of singular fractional differential equations with interval time-varying delay. Based on the proposed approach, new delay-dependent sufficient conditions such that the system is regular, impulse-free and finite-time stable are developed in terms of a tractable linear matrix inequality and the Mittag-Leffler function. A numerical example is given to illustrate the application of the proposed stability conditions.

中文翻译：

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具有时变延迟的奇异分数阶微分方程的新有限时间稳定性分析

摘要 李雅普诺夫函数法是泛函微分方程稳定性分析的有力工具。然而，该方法不适用于带时滞的分数阶微分方程，因为Lyapunov-Krasovskii函数的构造和分数阶导数的计算仍然很困难。在本文中，为了克服这个困难，我们提出了一种基于拉普拉斯变换和“inf-sup”方法的分析方法，研究具有区间时变延迟的奇异分数阶微分方程的有限时间稳定性。基于所提出的方法，根据易处理的线性矩阵不等式和 Mittag-Leffler 函数，开发了新的依赖于延迟的充分条件，使得系统是规则的、无脉冲的和有限时间稳定的。