Asymptotic and exponential stability of certain third-order non-linear delayed differential equations: frequency domain method
type: Item
instance of: scholarly article
title: Asymptotic and exponential stability of certain third-order non-linear delayed differential equations: frequency domain method
zbMATH Open document ID: 1200.34081
author: Jairo Eloy Castellanos
author: Anthony Uyi Afuwape
published in: Applied Mathematics and Computation
publication date: 2010-05-11T00:00:00Z
review text: The asymptotic stability of the zero solution for some third order delayed differential equations is studied by the frequency domain method. Also, for the non-homogeneous equations, the existence of exponentially stable bounded solutions is proved. The known theorems on absolute stability for the system of the form \[ \dot X(t)=AX(t)+BX(t-\tau)-Q\varphi(\sigma(t))+P(t),\quad \sigma(t)=C_1X(t)+C_2X(t) \] with sector conditions for \(\varphi\) are used to obtain the results.
reviewed by: Nataliya O. Sedova
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 5707074
zbMATH Keywords: third order delay differential equation
zbMATH Keywords: asymptotic stability
zbMATH Keywords: exponential stability
zbMATH Keywords: frequency domain method
MaRDI profile type: Publication
full work available at URL: j.amc.2010.01.109
OpenAlex ID: W2154825683
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DOI: 10.1016/J.AMC.2010.01.109
description: scientific article; zbMATH DE number 5707074