In this article, we consider the differential equation |$\dot{v}\left (t\right )=-q\left (t\right )\beta \left (v\left (t\right )\right )+e\left (t\right )$| and derive sufficient conditions for the convergence of its solution(s) when |$t\rightarrow \infty $|⁠. As an application, we give generalized sufficient conditions for the global attractivity and the global asymptotic stability of a class of time-varying systems. To illustrate the proposed results, the stability of the time-varying Lorenz system is studied.

中文翻译：

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一类时变微分方程的状态收敛

在本文中，我们考虑微分方程| $ \ dot {v} \ left（t \ right）=-q \ left（t \ right）\ beta \ left（v \ left（t \ right）\ right）+ e \ left（t \ right）$ | 并在| $ t \ rightarrow \ infty $ |⁠时得出足够的条件来收敛其解。作为一种应用，我们为一类时变系统的全局吸引性和全局渐近稳定性给出了广义的充分条件。为了说明所提出的结果，研究了时变Lorenz系统的稳定性。