Bipartite synchronization in coupled delayed neural networks under pinning control

This paper considers the bipartite leader-following synchronization in a signed network composed by an array of coupled delayed neural networks by utilizing the pinning control strategy and M-matrix theory, where the communication links between neighboring nodes of the network can be either positive or negative. Under the assumption that the node-delay is bounded and differentiable, a sufficient condition in terms of a low-dimensional linear matrix inequality is derived for reaching bipartite leader-following synchronization in the signed network, based on which a simple algebraic formula is further given to estimate an upper bound of the node-delay. When the node-delay is bounded and non-differentiable, some criteria are established by using the descriptor method and the reciprocally convex approach such that the bipartite leader-following synchronization problem for the signed network can be successfully solved. Finally, numerical simulations are provided to illustrate the effectiveness of theoretical analysis.