Technical communique: Finite-time stability theorem of stochastic nonlinear systems

Authors:
Weisheng Chen;L. C. Jiao
Affiliations:
Department of Applied Mathematics, Xidian University, Xi'an, 710071, PR China and Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Institute of I ...;Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Institute of Intelligent Information Processing, Xidian University, Xi'an, 710071, PR China
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

A new concept of finite-time stability, called stochastically finite-time attractiveness, is defined for a class of stochastic nonlinear systems described by the Ito differential equation. The settling time function is a stochastic variable and its expectation is finite. A theorem and a corollary are given to verify the finite-time attractiveness of stochastic systems based on Lyapunov functions. Two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper.