$$ \varvec{\alpha}$$-Path Stability Analysis for Uncertain Differential Equations

Abstract

The uncertain differential equation is a type of differential equations driven by Liu process. It has a wide application in field finance and optimal control. The $$ \alpha $$ -path method is a useful tool in studying uncertain differential equations. The stability property on the uncertain differential equation is an important aspect both in theory and in practice. In this paper, the concepts of $$ \alpha $$ -path stability for the uncertain differential equation are proposed. Furthermore, several stability theorems for uncertain differential equations are proved.