Global Synchronization of Directional Networked Systems With Eventually Dissipative Nodes

In the existing literature related to the global synchronization of networked systems, the V-uniformly decreasing condition on the nodal self-dynamics has often been assumed in advance. However this assumption excludes nonuniformly Lipschitz systems, such as the well-known Lorenz oscillators. In this paper, we adopt the eventual dissipativity condition to relax the V-uniformly decreasing condition such that the obtained results are applicable to some nonuniformly Lipschitz systems. Firstly the concept of synchronization degree is presented to depict the synchronizability of the nodal self-dynamics (NSD) system over its associated attractor. Then a virtual node whose trajectory is proved to ultimately evolve in the same region with that of isolated node is presented to play the reference trajectory. Next a simple global synchronization criterion that highlights the interplay between the NSD system and the network topology is presented, which can be applied for the reducible networks. Finally, a simulation example on a reducible network verifies the analytic results.