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. 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.
In this survey, we introduce the notion of stability of time varying nonlinear systems. In particular we investigate the notion of global practical exponential stability for non-autonomous systems. The proposed approach for stability analysis is based on the determination of the bounds of perturbations that characterize the asymptotic convergence of the solutions to a closed ball centered at the origin.
This paper deals with the problem of the global uniform stability of nonlinear time-varying systems in the presence of perturbations. The main novelty relies on the fact that the
proposed approach for stability analysis allows for the computation of the
bounds which characterize the asymptotic convergence of solutions
to a small ball centered at the origin. Therefore, we generalize some results which have already be announced in the
literature. Furthermore, we provide a numerical example to validate the effectiveness of our main result.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.