Almost Sure Stability for Multi-Dimensional Uncertain Differential Equations

Abstract

Multi-dimensional uncertain differential equation is a tool to model an uncertain multi-dimensional dynamic system. Furthermore, stability has a significant role in the field of differential equations because it can be describe the effect of the initial value on the solution of the differential equation. Hence, the concept of almost sure stability is presented concerning multi-dimensional uncertain differential equation in this paper. Moreover, a stability theorem, that is a condition, is derived to judge whether a multi-dimensional uncertain differential equation is almost surely stable or not. Additionally, the paper takes a counterexample to show that the given condition is not necessary for a multi-dimensional uncertain differential equation being almost surely stable.