Almost sure and pth moment stability of uncertain differential equations with time-varying delay

Abstract

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.