Stability of high-order uncertain differential equations

Article type: Research Article

Authors: Sheng, Yuhong^{; *}

Affiliations: College of Mathematical and System Sciences, Xinjiang University, Urumchi, China

Correspondence: [*] Corresponding author. Yuhong Sheng, College of Mathematical and System Sciences, Xinjiang University, Urumchi 830046, China. Tel.: +8618167978160; E-mail: sheng-yh12@mails.tsinghua.edu.cn.

Abstract: High-order uncertain differential equations are applied to model differentiable uncertain systems with high-order differentials. In order to describe the influence of the initial value on the solution, this paper proposes two concepts of stability for high-order uncertain differential equation, including stability in measure and stability in mean. Most important of all, some stability theorems are given for a high-order uncertain differential equation. In addition, this paper shows that the given condition is not necessary for a high-order uncertain differential equation being stable via a counterexample. Lastly, this paper will discuss the relationship between stability in measure and stability in mean.

Keywords: High-order uncertain differential equation, uncertain process, Liu process, stability

DOI: 10.3233/JIFS-17277

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 3, pp. 1363-1373, 2017