Open AccessLyapunov-Krasovskii stability analysis of nonlinear integro-differential equation
Author(s) -
Prebo Clifford Jackreece
Publication year - 2018
Publication title -
international journal of applied mathematical research
Language(s) - English
Resource type - Journals
ISSN - 2227-4324
DOI - 10.14419/ijamr.v7i2.10168
Subject(s) - mathematics , nonlinear system , stability (learning theory) , differential equation , integro differential equation , mathematical analysis , lyapunov function , exponential stability , differential (mechanical device) , class (philosophy) , first order partial differential equation , computer science , physics , quantum mechanics , machine learning , aerospace engineering , artificial intelligence , engineering
The purpose of this paper is to develop a qualitative stability analysis of a class of nonlinear integro-differential equation within the framework of Lyapunov-Krasovskii. We show that the existence of a Lyapunov-Krasovskii functional is a necessary and sufficient condition for the uniform asymptotic stability of the nonlinear Volterra integro-differential equations.