Synchronization of complex networks with coupling delay via pinning control
Xinsong Yang, Jinde Cao · IMA Journal of Mathematical Control and Information · 2015
This paper investigates global asymptotic synchronization for a class of complex networks with communication delay (time-delayed couplings). Both a time-delayed state feedback controller and time-delayed adaptive controller are designed. Several sufficient conditions formulated by linear matrix inequalities are derived. Our results show that the considered network can be synchronized onto an isolated node by adding the designed controllers to a small fraction of the coupled nodes (delayed pinning control). Moreover, it is found that (a) if the upper bound of the coupling delay is too large, then the coupled networks cannot be pinned to the synchronization state with any control gains, even if all the nodes are controlled; (b) the delayed pinning controller with either too low or too large control gains cannot realize the synchronization goal. Two examples are given to verify the theoretical results.