Open AccessAsymptotic behavior of a class of perturbed differential equations
Author(s) -
A. Dorgham,
Mekki Hammi,
Mohamed Ali Hammami
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i5.232
Subject(s) - exponential stability , mathematics , nonlinear system , lyapunov function , class (philosophy) , mathematical analysis , ball (mathematics) , differential equation , asymptotology , method of matched asymptotic expansions , physics , computer science , quantum mechanics , artificial intelligence
UDC 517.9This paper deals with the problem of stability of nonlinear differential equations with perturbations. Sufficient conditions for global uniform asymptotic stability in terms of Lyapunov-like functions and integral inequality are obtained. The asymptotic behavior is studied in the sense that the trajectories converge to a small ball centered at the origin. Furthermore, an illustrative example in the plane is given to verify the effectiveness of the theoretical results.