Weighted exponential stability of stochastic coupled systems on networks with delay driven by \begin{document}$ G $\end{document}-Brownian motion

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.