Generalized Lyapunov criteria on finite-time stability of stochastic nonlinear systems

被引：107
作者：
Yu, Xin [1 ]
Yin, Juliang [2 ]
Khoo, Suiyang [3 ]
机构：
[1] Jiangsu Univ, Sch Elect & Informat Engn, Zhenjiang, Jiangsu, Peoples R China
[2] Guangzhou Univ, Sch Econ & Stat, Guangzhou, Guangdong, Peoples R China
[3] Deakin Univ, Sch Engn, Geelong, Vic, Australia
来源：
AUTOMATICA | 2019年 / 107卷
基金：
中国国家自然科学基金;
关键词：
Finite-time stability; Generalized Lyapunov theorem; Multiple Lyapunov functions; Stochastic nonlinear systems; STABILIZATION; THEOREM;
D O I：
10.1016/j.automatica.2019.05.048
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 paper considers the problem of finite-time stability for stochastic nonlinear systems. A general Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing results are also given. This theorem not only generalizes the classical stochastic finite-time theorem, but also somewhat shows that Brownian noise takes an active role in stochastic finite-time stability. In addition, more general conditions on stochastic finite-time stability via multiple Lyapunov functions are given to further relax the constraint of the differential operator LV. Moreover, with the help of this criterion, it shows that an unstable deterministic system can even be finite-time stabilized by Brownian noise. Some concrete examples are constructed to show the significant features of the proposed results, and simulations are presented to verify the theoretical analysis. (C) 2019 Elsevier Ltd. All rights reserved.
引用
收藏
页码：183 / 189
页数：7
相关论文
共 26 条
[1]  
[Anonymous], 2012, STOCHASTIC STABILITY
[2]   Stabilization and destabilization of nonlinear differential equations by noise [J].
Appleby, John A. D. ;
Mao, Xuerong ;
Rodkina, Alexandra .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (03) :683-691
[3]  
Arnold L., 1974, STOCHASTIC DIFFERENT
[4]   Finite-time stability of continuous autonomous systems [J].
Bhat, SP ;
Bernstein, DS .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (03) :751-766
[5]   Finite-time stability theorem of stochastic nonlinear systems [J].
Chen, Weisheng ;
Jiao, L. C. .
AUTOMATICA, 2010, 46 (12) :2105-2108
[6]   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)
[7]   Global finite-time stabilization of a class of uncertain nonlinear systems [J].
Huang, XQ ;
Lin, W ;
Yang, B .
AUTOMATICA, 2005, 41 (05) :881-888
[8]   Stability of stochastic nonlinear systems in cascade with not necessarily unbounded decay rates [J].
Ito, Hiroshi ;
Nishimura, Yuki .
AUTOMATICA, 2015, 62 :51-64
[9]  
Khalil H.K., 2002, Non Linear System
[10]   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
123