Uncertain differential equation is a type of differential equation driven by Liu process that is the counterpart of Wiener process in the framework of uncertainty theory. The stability theory is of particular interest among the properties of the solutions to uncertain differential equations. In this paper, we introduce the Lyapunov’s second method to study stability in measure and asymptotic stability of uncertain differential equation. Different from the existing results, we present two sufficient conditions in sense of Lyapunov stability, where the strong Lipschitz condition of the drift is no longer indispensable. Finally, illustrative examples are examined to certify the effectiveness of our theoretical findings.

不确定微分方程是由Liu过程驱动的一类微分方程，在不确定性理论的框架内，它是Wiener过程的对应物。在不确定微分方程解的性质中，稳定性理论特别受关注。在本文中，我们介绍了Lyapunov的第二种方法来研究不确定微分方程的度量稳定性和渐近稳定性。与现有结果不同，我们在Lyapunov稳定性的意义上提出了两个充分条件，其中强漂移的Lipschitz条件不再是必不可少的。最后，研究了示例性实例以证明我们理论发现的有效性。