Mathematics, Vol. 11, Pages 1458: Event-Triggered Control for Intra/Inter-Layer Synchronization and Quasi-Synchronization in Two-Layer Coupled Networks

Mathematics, Vol. 11, Pages 1458: Event-Triggered Control for Intra/Inter-Layer Synchronization and Quasi-Synchronization in Two-Layer Coupled Networks

Mathematics doi: 10.3390/math11061458

Authors: Cheng Zhang Chuan Zhang Fanwei Meng Yi Liang

This paper studies the intra/inter-layer synchronization and quasi-synchronization in two-layer coupled networks via event-triggered control, in which different layers have mutually independent topologies. First, based on Lyapunov stability theory and event-triggered thoughts, hybrid controllers are designed, respectively, for intra-layer synchronization (ALS) and inter-layer synchronization (RLS). Second, a novel event-triggered rule is proposed, under which intra-layer quasi-synchronization (ALQS) and inter-layer quasi-synchronization (RLQS) can be respectively realized, and the event-triggered frequency can be greatly reduced. Moreover, the upper bound of the synchronization error can be flexibly adjusted by changing the parameters in event-triggered conditions, and the Zeno phenomenon about event-triggered control is also discussed in this paper. Finally, numerical examples are provided to confirm the correctness and validity of the proposed scheme.