Synchronization between two complex dynamical networks with time delay coupling and circumstance noise

The synchronization between two complex networks with time delay coupling and circumstance noise in the transmission channel is studied in this paper. Two kinds of networks are studied including states coupled and outputs coupled. In order to suppress the effect introduced by the noise, the synchronization controllers are designed by using the integral control approach. Some sufficient conditions of synchronization between two complex networks are derived in the form of linear matrix inequalities (LMIs) by using Lyapunov stability theory and H_∞ control approach. The synchronization errors are convergent to zeros with H_∞ performance index. Finally, two numerical examples are given to demonstrate the validity and effectiveness of the controllers proposed in the paper.