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Abstract：
Stability in distribution for uncertain delay differential equations based on the strong Lipschitz condition only involving the current state has been successfully investigated. In reality, the uncertain delay differential equation is not only relate to the current state, but also relate to the past state, so it is very hard to obtain the strong Lipschitz condition. In this paper, the new Lipschitz condition concerning the current state and the past state is provided, if the uncertain delay differential equation satisfies the strong Lipschitz condition, it must satisfy the new Lipschitz condition, conversely, it may not be established. By means of the new Lipschitz condition, a sufficient theorem for the uncertain delay differential equation being stable in distribution is proved. Meanwhile, a class of uncertain delay differential equation is certified to be stable in distribution without any limited condition. Besides, the effectiveness of the above sufficient theorem is verified by two numerical examples.
摘要：
已成功研究了仅涉及当前状态的基于强Lipschitz条件的不确定延迟微分方程的分布稳定性。在现实中,不确定延迟微分方程不仅与当前状态有关，但也与过去的状态有关，所以很难获得强烈的Lipschitz条件。在本文中,提供了关于当前状态和过去状态的新Lipschitz条件，如果不确定时滞微分方程满足强Lipschitz条件，它必须满足新的Lipschitz条件，相反,它可能无法建立。通过新的Lipschitz条件,证明了不确定时滞微分方程分布稳定的一个充分定理。同时,证明了一类不确定时滞微分方程在没有任何限制条件的情况下是稳定的。此外,两个数值算例验证了上述充分定理的有效性。
