Open AccessDelay‐dependent stability of a class of stochastic delay systems driven by G‐Brownian motion
Author(s) -
Yao Shenghao,
Zong Xiaofeng
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.1146
Subject(s) - mathematics , control theory (sociology) , brownian motion , stability (learning theory) , sublinear function , lyapunov function , exponential stability , degenerate energy levels , mathematical analysis , computer science , nonlinear system , physics , statistics , control (management) , artificial intelligence , machine learning , quantum mechanics
This study discusses delay‐dependent stability of a class of stochastic delay systems driven by G‐Brownian motion in the sublinear expectation space. With the help of the degenerate Lyapunov functional, the mean square exponential stability and quasi‐sure exponential stability criteria for stochastic delay systems driven by G‐Brownian motion are established and an explicit upper bound of time delay is derived. In particular, for the delay‐free case, the corresponding sufficient conditions are also obtained. Here, the stability conditions are directly related to the coefficients of the stochastic delay systems and are different from the existing stability conditions which are presented in terms of the G‐Lyapunov function. Some examples are introduced to illustrate the delay‐dependent stability criteria.