Adaptive synchronization of noise-perturbed complex delayed network systems

Concerning the effect of internal noise and communication delay in the synchronized process, we introduce a noise-perturbed complex network dynamical model and design an adaptive feedback controller to synchronize the proposed network. Based on invariance principle of stochastic time-delay differential equations, a sufficient condition in terms of linear matrix inequality is derived to guarantee global synchronization of the network via the adaptive controller. The analytical results show that the adaptive control scheme is of robustness against the noise resulted from the internal synchronized errors. Finally, a numerical simulation is provided to verify the effectiveness of the adaptive strategy.