Leader-following consensus of delayed neural networks under multi-layer signed graphs

Abstract

This paper considers the leader-following consensus problem for delayed neural networks with multi-layer signed digraph topologies. Both structurally balanced and unbalanced topologies are considered. By using the structural balance theory and the pinning control strategy, some sufficient conditions are given to guarantee that the bipartite leader-following consensus can be reached in structurally balanced multi-layer signed neural networks, which depend on the node dynamics and the topology of the multi-layer signed network. In addition, a scheme is designed for selecting the pinning nodes and gains of each layer to achieve bipartite leader-following consensus. When the multi-layer signed network is structurally unbalanced, the asymptotic stability of the neural network is investigated by decomposing the structurally unbalanced network into a structurally balanced subgraph and some special edges. The conditions proposed in this paper are also suitable for addressing the consensus problem of traditional single layer signed neural networks. Numerical examples are given to illustrate the correctness and effectiveness of the proposed theorems and algorithms.