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.

中文翻译：

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非自治微扰动力系统均匀指数稳定性的新结果

在本文中，我们研究了当标称部分受到不必要的小扰动时，平衡点附近非线性动态系统解的渐近行为。我们表明，在对扰动项的某些估计下，平衡点保持（全局）均匀指数稳定。获得的稳定性结果可以很容易地应用于实践，因为它们基于 Gronwall-Bellman 不等式，而不是需要 Lyapunov 函数知识的经典 Lyapunov 方法。图中给出了几个数值示例，以及在控制和机械系统中的应用。