Exponential stability of uncertain differential equation with jumps

Article type: Research Article

Authors: Liu, Shiqin^{; *}

Affiliations: College of Mathematics and Computer Science, Hengshui University, Hebei, China

Correspondence: [*] Corresponding author. Shiqin Liu, College of Mathematics and Computer Science, Hengshui University, Hebei 053000, China. E-mail: liushiqin168@163.com.

Abstract: Uncertain differential equation with jumps is a type of uncertain differential equation driven by both Liu process and uncertain renewal process. Many concepts of stability for uncertain differential equation with jumps have been investigated. This paper presents a concept of exponential stability for uncertain differential equations with jumps, and gives a sufficient and necessary condition for the linear uncertain differential equation with jumps being exponentially stable. The relationships among stability in measure, stability in in mean, stability in p-th moment, and almost sure stability for uncertain differential equation are also discussed.

Keywords: Uncertain differential equation, exponential stability, uncertainty theory

DOI: 10.3233/JIFS-190771

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 5, pp. 6891-6898, 2019