Synchronization in general complex dynamical networks with coupling delays

Complex networks have attracted increasing attention from various fields of science and engineering today. Due to the finite speeds of transmission and spreading as well as traffic congestions, a signal or influence travelling through a complex network often is associated with time delays, and this is very common in biological and physical networks. In this paper, we introduce complex dynamical network models with coupling delays for both continuous- and discrete-time cases and then investigate their synchronization phenomena and criteria. Based on these new complex network models, we derive synchronization conditions for both delay-independent and delay-dependent asymptotical stabilities in terms of linear matrix inequalities (LMI). We finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results.