Fixed-time stability theorem of stochastic nonlinear systems

• Published in: International journal of control Vol. 92; no. 9; pp. 2194 - 2200
• Main Authors: Yu, Jiaju, Yu, Shuanghe, Li, Juan, Yan, Yan
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.09.2019; Taylor & Francis Ltd
• Subjects: Differential equations; fixed-time stability; infinitesimal generator; Lyapunov function; Nonlinear systems; Probability theory; Stability; stochastic nonlinear systems; stochastic settling time function; Stochastic systems; Theorems
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2018.1430900

To solve the fixed-time stability problem for stochastic systems, which has not been investigated due to the difficulty caused by the existence of stochastic, the fixed-time stability is investigated for stochastic nonlinear systems described by the It differential equation in this note. The main contributions exist in: (1) A new concept, fixed-time stable in probability, is proposed, and the detailed definition is given. (2) A criterion theorem is proposed to judge the fixed-time stable in probability, in addition, several corollaries are given for proving the fixed-time stability in probability for stochastic nonlinear systems. Two simulation examples are given to verify the proposed theoretical results in this paper.