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Cubo (Temuco)

versão On-line ISSN 0719-0646

Cubo vol.17 no.3 Temuco  2015

http://dx.doi.org/10.4067/S0719-06462015000300004 

Gronwall-Bellman type integral inequalities and applications to global uniform asymptotic stability

 

Mekki Hammi and Mohamed Ali Hammami

University of Sfax, Faculty of Sciences of Sfax, Department of Mathematics, Route Soukra, BP 1171, 3000 Sfax, Tunisia, mohamedali.hammami@fss.rnu.tn


ABSTRACT

In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities are established. These inequalities can be used as handy tools to research stability problems of perturbed dynamic systems. As applications, based on these new established inequalities, some new results of practical uniform stability are also given. A numerical example is presented to illustrate the validity of the main results.

Keywords and Phrases: Gronwall-Bellman inequality, perturbed systems, stability.
2010 AMS Mathematics Subject Classification: 26D15, 26D20, 34A40, 34H15.


RESUMEN

En este artículo, establecemos algunas desigualdades integrales nolineales nuevas de tipo Gronwall-Bellman. Estas desigualdades pueden ser usadas como herramientas utiles para estudiar problemas de estabilidad de sistemas dinámicos perturbados. Como aplicaciones, basados en las nuevas desigualdades establecidas, también damos algunos resultados nuevos de estabilidad uniforme prácticos. Un ejemplo numérico es presentado para ilustrar la validez de los resultados principales.


 

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Received: September 2013. Accepted: February 2015.

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