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Abstract

Uncertain differential equation plays an important role in dealing with dynamical systems with uncertainty. Multi-dimensional uncertain differential equation is a type of differential equation driven by multi-dimensional Liu processes. Stability analysis of a multi-dimensional means insensitivity of the state of a system to small changes in the initial state. This paper focuses on the stability in p-th moment for multi-dimensional uncertain differential equation. The concept of stability in p-th moment for multi-dimensional uncertain differential equation is presented. Some stability theorems for the solution of multi-dimensional uncertain differential equation are given, in which some sufficient conditions for a multi-dimensional uncertain differential equation being stable in p-th moment and a sufficient and necessary condition for a linear multi-dimensional uncertain differential equation being stable in p-th moment are provided. In addition, this paper discusses the relationships among stability in p-th moment, stability in measure and stability in mean.

Keywords

Uncertainty theory multi-dimensional uncertain differential equation moment stability

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Stability in p -th moment of multi-dimensional uncertain differential equation

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