The pth moment exponential stability of uncertain differential equation

Abstract

Uncertain variable and uncertain process are often employed to describe uncertainty phenomena. Uncertain variable is a measurable function from an uncertainty space to the real number set and uncertain process is essentially a sequence of uncertain variables indexed by time. Uncertain differential equation is a type of differential equation involving uncertain processes. Stability of an uncertain differential equation plays a very important role in differential equation which means insensitivity of the state of a system to small changes in the initial state. In this paper, we focus on pth moment exponential stability of uncertain differential equation which is regarded as an extension of pth moment stability and exponential stability. Some stability theorems are given for uncertain differential equation, in which a sufficient and necessary condition for a linear uncertain differential equation being pth moment exponentially stable is provided.