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Zbl 1235.93254
Yin, Juliang; Khoo, Suiyang; Man, Zhihong; Yu, Xinghuo
Finite-time stability and instability of stochastic nonlinear systems. (English)
[J] Automatica 47, No. 12, 2671-2677 (2011). ISSN 0005-1098

Summary: 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.

MSC 2000:: *93E15 Stochastic stability
93C10 Nonlinear control systems

Keywords: finite-time stability; Lyapunov stability; finite-time attractiveness in probability; stochastic nonlinear systems

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