Synchronization of Two-Layer Network with Directed Topologies Under Stochastic Control

In this paper, we investigate the synchronization problem of a two-layer network, consisting of an information exchange layer and a noise diffusion layer, each with different directed topologies. A new stochastic control is proposed and the conditions for the stochastic synchronization of the two-layer network are derived through stochastic Lyapunov method and the extension of algebraic connectivity in directed graphs. The effect of noise on network synchronization is also considered, and it is demonstrated through a simulation example that noise can induce network synchronization. This also demonstrates the advantages of stochastic control over traditional control. Finally, future research directions are proposed and the main results are summarized.