Title of article :
Finite-time stability and instability of stochastic nonlinear systems
Author/Authors :
Yin، نويسنده , , Juliang and Khoo، نويسنده , , Suiyang and Man، نويسنده , , Zhihong and Yu، نويسنده , , Xinghuo، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2011
Abstract :
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.
Keywords :
Finite-time stability , Finite-time attractiveness in probability , Stochastic nonlinear systems , Lyapunov Stability
Journal title :
Automatica
Journal title :
Automatica