Mixed-Delay-Based Augmented Functional for Sampled-Data Synchronization of Delayed Neural Networks With Communication Delay

The synchronization control for delayed neural networks (DNNs) via a sampled-data controller considering communication delay is studied by input delay approach. Although few scholars have put forward the coexistence of transmission delay and communication delay in this problem, no report has clarified the interaction between transmission delay and communication delay. Also, the time-squared terms are underutilized. Thus, a novel augmented Lyapunov functional, which consists of a mixed-delay-based augmented part and a time-squared two-sided looped part, is proposed to fill this gap. In the mixed-delay-based augmented part, not only the information of transmission delay and communication delay themselves, but also the interaction between those two delays is considered. Time-dependent quadratic terms as well as the sampling integral states are introduced in the two-sided looped part, so that more characteristic information of the sampling pattern is encompassed and the relationship of the states at the sampling instant is enhanced. Then, this novel augmented functional is applied to the synchronization control of DNNs. A less conservative synchronization criterion is obtained in the form of linear matrix inequalities. A numerical example illustrates the validity and superiority of the presented synchronization criterion.