Synchronization analysis for static neural networks with hybrid couplings and time delays

This paper deals with the synchronization problem for delayed static neural networks with hybrid couplings. When the static neural networks are affected by hybrid couplings, it is hard to deal with a large number of highly interconnected dynamical units in such a complex system. In order to solve this complicated problem, a new method is proposed to deal with the Kronecker product, and to make the synchronization problem to be easily analyzed. Further, based on the obtained result, by using the augmented Lyapunov-Krasovskii functional (LKF) method, multitude Kronecker product terms can be handled, which can introduce more relaxed conditions by employing the new type of augmented matrices with the Kronecker product operation. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed synchronization scheme.