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New finite-time stability analysis of singular fractional differential equations with time-varying delay
Fractional Calculus and Applied Analysis ( IF 3.170 ) Pub Date : 2020-04-28 , DOI: 10.1515/fca-2020-0024
Nguyen T. Thanh, Vu N. Phat, Piyapong Niamsup

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:

具有时变时滞的奇异分数阶微分方程的新有限时稳定性分析

Lyapunov函数方法是功能微分方程稳定性分析的强大工具。但是,由于建立Lyapunov-Krasovskii函数和计算其分数导数仍然很困难,因此该方法不能有效地应用于带延迟的分数阶微分方程。在本文中,为克服这一困难,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,以研究具有间隔时变时滞的奇异分数阶微分方程的有限时间稳定性。基于提出的方法,根据可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,从而使系统规则,无脉冲且具有有限时间稳定性。
更新日期:2020-04-28
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