New Exponential Stability Criteria for Certain Neutral Integro-Differential Equations

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 119 - 131, 28.02.2020

Melek Gözen

https://doi.org/10.18185/erzifbed.638208

Abstract

Bu çalışmada, birinci basamaktan
ayrık ve değişken gecikmeli neutral integro- diferansiyel denklemlerin (NIDE)
sıfır çözümünün üstel kararlılığı incelenmektedir. Uygun bir Lyapunov-Krasovski
fonksiyeli, Leibniz-Newton formülü ve matris eşitsizliği yardımıyla ele alınan
denklemin sıfır çözümünün üstel kararlılığı için yeter şartlar içeren yeni bir
sonuç ispatlanmaktadır. Bu çalışma literatürdeki konuyla ilgili önceki
sonuçları genişletmekte ve geliştirmektedir.

Keywords

Neutral differential equation, first order, exponential stability, time-varying delay, the direct method of Lyapunov

New Exponential Stability Criteria for Certain Neutral Integro-Differential Equations

Abstract

In this work, the exponential stability of zero solution of some neutral integro-differential equations of the first order (NIDE) with discrete and distributed time-varying delays is discussed. A new result that has sufficient conditions on the exponential stability of zero solution is proved by aid a new Lyapunov-Krasovskii functional, the Leibniz-Newton formula and a matrix inequality. The result of this paper extends and improves some former results on the topic in the literature.

Keywords

Neutral differential equation, first order, exponential stability, time-varying delay, direct method of Lyapunov

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