ABSTRACT

Uncertain differential equations with time-varying delay are a special type of uncertain functional differential equation. Stability in measure and stability in mean for this type of differential equation have been investigated. For the sake of completeness, this article explores the other two types of stability. Firstly, the concepts of the almost sure stability and the pth moment stability of uncertain differential equations with time-varying delay are proposed. Next, sufficient conditions, in the form of theorems, for uncertain differential equations with time-varying delay to be stable almost surely and in pth moment are deduced. Finally, the relationships between several types of stability for uncertain differential equations with time-varying delay are discussed.

摘要

时变时滞不确定微分方程是一类特殊的不确定泛函微分方程。已经研究了这类微分方程的测量稳定性和均值稳定性。为了完整起见，本文探讨了其他两种类型的稳定性。首先，提出了时变时滞不确定微分方程的几乎肯定稳定性和p阶矩稳定性的概念。接着，以定理的形式推导出时变时滞不确定微分方程在p时刻几乎肯定稳定的充分条件。最后，讨论了具有时变时滞的不确定微分方程几种稳定性之间的关系。