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

被引：43

作者：

Min, Huifang ^{[1
]}

Shi, Shang ^{[2
]}

Xu, Shengyuan ^{[1
]}

Guo, Jian ^{[1
]}

Zhang, Zhengqiang ^{[3
]}

机构：

[1] Nanjing Univ Sci & Technol, Sch Automat, Nanjing, Peoples R China

[2] Hohai Univ, Coll Energy & Elect Engn, Nanjing 211100, Peoples R China

[3] Qufu Normal Univ, Sch Elect Engn & Automat, Rizhao 276826, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2023年 / 68卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Fixed-time stability; Lyapunov theorem; practi-cally fixed-time stability in probability (PFxTSp); stochastic non-linear systems; FINITE-TIME; STABILITY THEOREM; STABILIZATION;

D O I：

10.1109/TAC.2022.3218592

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

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.

引用

页码：5052 / 5058

页数：7

共 25 条

[1] Authors' reply to "Comments on 'Finite-time stability theorem of stochastic nonlinear systems [Automatica 46 (2010) 2105-2108]'" [J].

Chen, Weisheng ;

Jiao, L. C. .

AUTOMATICA, 2011, 47 (07) :1544-1545

[2] Finite-time stability theorem of stochastic nonlinear systems [J].

Chen, Weisheng ;

Jiao, L. C. .

AUTOMATICA, 2010, 46 (12) :2105-2108

[3] Finite-time consensus protocol for stochastic multi-agent systems [J].

Chen, Xiurong ;

Li, Juan ;

Wu, Ziku ;

Yu, Jiashang .

IET CONTROL THEORY AND APPLICATIONS, 2019, 13 (06) :755-762

[4] Stabilization of stochastic nonlinear systems driven by noise of unknown covariance [J].

Deng, H. ;

Krstić, M. ;

Williams, R.J. .

1600, Institute of Electrical and Electronics Engineers Inc. (46)

[5] Global fixed-time stabilization for a class of switched nonlinear systems with general powers and its application [J].

Gao, Fangzheng ;

Wu, Yucliang ;

Zhang, Zhongcai ;

Liu, Yanhong .

NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2019, 31 :56-68

[6]

Has'minskii R., 1980, STOCHASTIC STABILITY

[7] Finite-Time Stabilization of Stochastic High-Order Nonlinear Systems With FT-SISS Inverse Dynamics [J].

Jiang, Meng-Meng ;

Xie, Xue-Jun ;

Zhang, Kemei .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2019, 64 (01) :313-320

[8]

Khalil H. K., 1996, Nonlinear Systems

[9] Finite-time stabilization of stochastic nonlinear systems in strict-feedback form [J].

Khoo, Suiyang ;

Yin, Juliang ;

Man, Zhihong ;

Yu, Xinghuo .

AUTOMATICA, 2013, 49 (05) :1403-1410

[10]

_ksendal B., 2010, STOCHASTIC DIFFERENT, V6

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