Synchronization in Arrays of Neural Networks with Distributed Delays and Coupling

Abstract In this paper, the global exponential synchronization in arrays of neural networks with distributed delays and coupling is investigated. Without assuming the inner coupling matrix to be diagonal, by employing a new Lyapunov-Krasovskii functional, applying the theory of Kronecker product of matrices and the linear matrix inequality (LMI) technique, a sufficient conditions in LMI form is obtained for global exponential synchronization of such systems. Moreover, the exponential convergence index is estimated. The proposed LMI approach has the advantage of considering the difference of neuronal excitatory and inhibitory efforts, which is also computationally efficient as it can be solved numerically using efficient Matlab LMI toolbox, and no tuning of parameters is required. An example is given to show the effectiveness of the obtained results.