Finite-time stability theorem of stochastic nonlinear systems

• Published in: Automatica (Oxford) Vol. 46; no. 12; pp. 2105 - 2108
• Main Authors: Chen, Weisheng, Jiao, L.C.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.12.2010; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Differential equations; Dynamical systems; Exact sciences and technology; Finite-time stability; Lyapunov functions; Lyapunov method; Nonlinear dynamics; Stability; Stochastic nonlinear systems; Stochastic settling time function; Stochastic systems; Stochasticity; Theorems; Lyapunov method; Stochastic settling time function; Finite-time stability; Stochastic nonlinear systems; Itô equation; Stability; Probabilistic approach; Differential equation; Non linear control; Non linear system; Uncertain system; Non deterministic system; Lyapunov function
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2010.08.009

A new concept of finite-time stability, called stochastically finite-time attractiveness, is defined for a class of stochastic nonlinear systems described by the Itô 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.