Fixed-Time Lyapunov Criteria of Stochastic Nonlinear Systems and Its Generalization

• 成果类型: Article
• 署名作者: Min, Huifang; Shi, Shang; Xu, Shengyuan; Guo, Jian; Zhang, Zhengqiang
• 署名单位: Nanjing University of Science & Technology; Hohai University; Qufu Normal University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3218592
• 发表日期: 2023
• 页码: 5052-5058
• 关键词: Fixed-time stability; Lyapunov theorem; practi-cally fixed-time stability in probability (PFxTSp); stochastic non-linear systems

摘要

This study investigates the fixed-time stability of stochastic nonlinear systems described by Ito differential equations. The improved fixed-time Lyapunov theorem is given and an important corollary is obtained. It is proved that the upper-bound estimate of the settling time is less conservative. We establish a new definition of practically fixed-time stability in probability and propose the corresponding Lyapunov criterion theorem. In addition, different cases of the parameters are discussed to provide a less conservative upper-bound estimate of the settling time. The effectiveness of the proposed stability and controller is demonstrated by two simulation examples.