Graph-theoretic approach to exponential synchronization of discrete-time stochastic coupled systems with time-varying delay

In this paper, we investigate the exponential synchronization problem for discrete-time stochastic drive-response coupled systems with time-varying delay. By employing the Lyapunov method combined with Kirchhoff's matrix tree theorem in graph theory as well as stochastic analysis technique, some novel sufficient criteria are established to guarantee the exponential synchronization of two identical delayed coupled systems with stochastic disturbances. These sufficient criteria have a close relationship with the topological property of the coupled network. Moreover, the theoretical results are applied to a coupled oscillators system to demonstrate the applicability of the proposed synchronization approaches. Finally, a numerical example is provided to illustrate the effectiveness of our theoretical results.