In this paper, we establish the sufficient conditions guaranteeing global uniform exponential stability, or at least global asymptotic stability, of all solutions for nonlinear dynamical systems, also known as global incremental stability (GIS) of the systems. We provide here an alternative approach for assessment of GIS in terms of logarithmic norm under which the stability becomes a topological notion and also generalize both horizontally and vertically the well-known Demidovich criterion for GIS of dynamical systems. Convergence of all solutions to the origin $x=0,$ which is not assumed to be an equilibrium state of system, is also analyzed. Theory is illustrated by a simulation experiment.

在本文中，我们建立了保证非线性动力系统的所有解的全局均匀指数稳定性或至少是全局渐近稳定性的充分条件，也称为系统的全局增量稳定性（GIS）。我们在这里提供了一种根据对数范数评估 GIS 的替代方法，在这种方法下，稳定性成为一个拓扑概念，并在水平和垂直方向上推广了众所周知的动态系统 GIS 的 Demidovich 标准。所有解的收敛于原点$X=0,$不假定是系统的平衡状态，也进行了分析。通过模拟实验说明理论。