New stability theorems of uncertain differential equations with time-dependent delay

Abstract

Stability in measure and stability in mean for uncertain differential equations with time-dependent delay have been investigated, which are not applicable for all situations, for the sake of completeness, this paper mainly gives the concepts of stability almost surely, in p-th moment and in distribution, and proves the sufficient conditions for uncertain differential equations with time-dependent delay being stable almost surely, in p-th moment and in distribution, respectively. In addition, the relationships among stability in measure, stability in p-th moment, and stability in distribution for the uncertain differential equation with time-dependent delay are also discussed.

Keywords

• uncertain differential equations with time-dependent delay
• stability almost surely
• stability in <i>p</i>-th moment
• stability in distribution