  In this paper, we investigate the asymptotic behaviors of the solutions of
nonlinear dynamic systems nearby an equilibrium point, when the nominal parts
are subject to non necessarily small perturbations. We show that, under some
estimates on the perturbation terms, the equilibrium point remains (globally)
uniformly exponentially stable. The results we obtained can easily be applied
in practice since they are based on the Gronwall-Bellman inequalities rather
than the classical Lyapunov methods that require the knowledge of a Lyapunov
function. Several numerical examples are presented in order to illustrate the
validity of our study, especially when the standard Lyapunov approaches are
useless.
