Weighted exponential stability of stochastic coupled systems on networks with delay driven by $ G $ -Brownian motion
Yong Ren, Huijin Yang, Wensheng Yin · Discrete and Continuous Dynamical Systems - B · 2019
This paper investigates the issue of weighted exponentially input to state stability (EISS, in short) of stochastic coupled systems on networks with time-varying delay driven by \begin{document}$ G $\end{document} -Brownian motion ( \begin{document}$ G $\end{document} -SCSND, in short). Combining with inequality technique, \begin{document}$ k $\end{document} th vertex-Lyapunov functions and graph-theory, we establish the weighted EISS for \begin{document}$ G $\end{document} -SCSND. An application to the EISS for a class of stochastic coupled oscillators networks with control inputs driven by \begin{document}$ G $\end{document} -Brownian motion and an example are provided to illustrate the effectiveness of the obtained theory.