期刊
AUTOMATICA
卷 47, 期 12, 页码 2671-2677出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2011.08.050
关键词
Finite-time stability; Lyapunov stability; Finite-time attractiveness in probability; Stochastic nonlinear systems
资金
- Natural Science Foundation of China [61174212]
- Natural Science Foundation of Guangdong [10151063201000042]
This paper presents a new definition of finite-time stability for stochastic nonlinear systems. This definition involves stability in probability and finite-time attractiveness in probability. An important Lyapunov theorem on finite-time stability for stochastic nonlinear systems is established. A theorem extending the stochastic Lyapunov theorem is also proved. Moreover, an example and a lemma are presented to illustrate the scope of extension. A useful inequality, extended from Bihari's inequality, is derived, which plays an important role in showing the Lyapunov theorem. Finally, a Lyapunov theorem on finite-time instability is proved, which states that almost surely globally asymptotical stability is not equivalent to finite-time stability for some stochastic systems. Two simulation examples are given to illustrate the theoretical analysis. Crown Copyright (C) 2011 Published by Elsevier Ltd. All rights reserved.
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