Crossed Synchronization of Multiple Subnets Complex Network System with Time-Varying Delay

A dual-time varying delay complex network system is formed by a plurality of sub-networks. This paper discusses the crossed synchronization stability of such systems on the basis of crossed synchronization definition between the sub-nets. By the Lyapunov stability theory with the Zero Theorem, we obtained a sufficient condition that a synchronization exponentially stable controller exists in the complex network system, with characteristic variable delay. The relationship between the complex network nodes are discussed, and the two nodes must be connected and can interact with each other so it has the actual coupling strength. Finally, combining the given conditions, a numerical simulation illustrates its effectiveness.