Finite-time stability theorems of homogeneous stochastic nonlinear systems

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• 作者：Juliang Yin^a ; ^{yin_juliang@hotmail.com} ; Suiyang Khoo^b ; ^{sui.khoo@deakin.edu.au} ; Zhihong Man^c ; ^{zman@swin.edu.au}
• 关键词：Finite-time stochastic stability ; Stochastic nonlinear systems ; Homogeneity ; Homogeneous Lyapunov functions
• 刊名：Systems & Control Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：100
• 期：Complete
• 页码：6-13
• 全文大小：554 K
• 卷排序：100

文摘

The purpose of this paper is to study finite-time stability of a class of homogeneous stochastic nonlinear systems modeled by stochastic differential equations. An existence result of weak solutions for stochastic differential equations with continuous coefficients is derived as a preparation for discussing stochastic nonlinear systems. Then a generalization of finite-time stochastic stability theorem is given. By using some properties of homogeneous functions and homogeneous vector fields, it is proved that a homogeneous stochastic nonlinear system is finite-time stable if its coefficients have negative degrees of homogeneity, and there exists a sufficiently smooth and homogeneous Lyapunov function such that the infinitesimal generator of the stochastic system acting on it is negative definite. In the case when the drift coefficient of a stochastic system is homogeneous and has a negative degree of homogeneity, it can be shown that the stochastic system is also finite-time stable under appropriate conditions. Two examples are provided as illustrations.