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New results on the uniform exponential stability of nonautonomous perturbed dynamical systems

In this article, 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 term, the equilibrium point remains (globally) uniformly exponentially stable. The obtained stability results 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, as well as an application to control and mechanical systems, are given in illustration.