The generalized synchronization for double-layer delayed coupling complex networks by dynamic soft variable structure control method

This study focuses on the synchronization problem of double-layer complex networks with time delayed coupling. Distinguish from most of previous works, a more general network model is introduced, where the number and the dimension of the nodes can be different between the drive network and the response network. This network model is more close to the practice. In order to obtain the synchronization of double-layer complex networks, an ingenious dynamic soft variable structure controller is proposed, where three sub-controllers and one adaptive observers are designed, and the stability of the controller is demonstrated by a strict mathematical proof. Numerical simulations verify the effectiveness of proposed strategy.