Abstract We propose a new approach to studying the global asymptotic stability of an equilibrium position of a system of ordinary differential equations with respect to part of the variables. New functions, different from Lyapunov ones, are used to study state trajectories of systems of ordinary differential equations and prove the global stability theorem. An application of the theorem to proving the global stability for some systems of ordinary differential equations studied by Krasovskii and Pliss is considered.

中文翻译：

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关于常微分方程组解的部分变量的全局渐近稳定性

摘要 我们提出了一种研究常微分方程组关于部分变量的平衡位置的全局渐近稳定性的新方法。不同于李雅普诺夫函数的新函数用于研究常微分方程组的状态轨迹并证明全局稳定性定理。考虑了该定理在证明 Krasovskii 和 Pliss 研究的某些常微分方程组的全局稳定性中的应用。