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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Growth Conditions for Asymptotic Behavior of Solutions for Certain Time-varying Differential Equations

Author(s):

H. Damak

University of Sfax Tunisia,
Faculty of Science of Sfax, Department of Mathematics

M. A. Hammami

University of Sfax Tunisia,
Faculty of Science of Sfax, Department of Mathematics

MohamedAli.Hammami@fss.rnu.tn

A. Kicha

University of Sfax Tunisia,
Faculty of Science of Sfax, Department of Mathematics

Abstract:

The question proposed in this paper is related to the study of the preservation of uniform h-stability and uniform boundedness of time-varying nonlinear differential equations with a perturbation using Gronwall's inequalities and Lyapunov's theory. Moreover, we show the linearization technique for the uniform h-stability of a nonlinear system and give necessary and sufficient conditions for the global boundedness of perturbed systems. The last part is devoted to the study of the problem of h-stabilization for certain classes of nonlinear systems. Some examples and simulations are given to illustrate the main results.

Keywords

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