Fixed-time stability theorem of stochastic nonlinear systems. Issue 9 (2nd September 2019)

• Record Type: Journal Article
• Authors: Yu, Jiaju; Yu, Shuanghe; Li, Juan; Yan, Yan
• Is Part Of: International journal of control. Volume 92:Issue 9(2019)
• Page Start: 2194
• Page End: 2200
• Publication Date: 2019-09-02
• Subjects: fixed-time stability -- stochastic nonlinear systems -- infinitesimal generator -- stochastic settling time function -- Lyapunov function; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1430900
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: 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 o ^ 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.