Exponential stability of uncertain differential equation
Exponential stability of uncertain differential equation
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DOI：
10.1007/s00500-015-1727-0
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发表时间：
2015-06
期刊：
影响因子：
4.1
通讯作者：
Y. Sheng;Jinwu Gao
中科院分区：
文献类型：
--
作者：
Y. Sheng;Jinwu Gao
不确定微分方程是一类涉及不确定过程的微分方程。到目前为止，对于不确定微分方程已经提出了测度稳定性和平均稳定性的概念。本文提出了一类新的不确定微分方程的稳定性，称为指数稳定性。给出了一些例子来说明这一概念，并讨论了指数稳定性、依测度稳定性和依均值稳定性之间的关系。此外，还得到了一类线性不确定微分方程指数稳定的一个充分必要条件。
Uncertain differential equation is a type of differential equations involving uncertain processes. So far, the concepts of stability in measure and stability in mean have been proposed for uncertain differential equations. This paper proposes a new type of stability for uncertain differential equation, named exponential stability. Some examples are given to illustrate the concept, and the relationships between exponential stability, stability in measure and stability in mean are discussed. Besides, a sufficient and necessary condition for a linear uncertain differential equation being exponentially stable is derived.