Synchronization for an array of neural networks with hybrid coupling by a novel pinning control strategy

In this paper, a novel pinning synchronization (synchronization with pinning control) scheme for an array of neural networks with hybrid coupling is investigated. The main contributions are as follows: (1) A novel pinning control strategy is proposed for the first time. Pinning control schemes are introduced as an array of column vector. The controllers are designed as simple linear systems, which are easy to be analyzed or tested. (2) Augmented Lyapunov–Krasovskii functional (LKF) is applied to introduce more relax variables, which can alleviate the requirements of the positive definiteness of the matrix. (3) Based on the appropriate LKF, by introducing some free weighting matrices, some novel synchronization criteria are derived. Furthermore, the proposed pinning control scheme described by column vector can also be expanded to almost all the other array of neural networks. Finally, numerical examples are provided to show the effectiveness of the proposed results.