Stability in distribution for uncertain delay differential equations based on new Lipschitz condition.

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.