H∞ synchronization of coupled reaction-diffusion neural networks with mixed delays

The reaction-diffusion neural network is often described by semilinear diffusion partial differential equation (PDE). This article focuses on the asymptotical synchronization and H∞synchronization for coupled reaction-diffusion neural networks with mixed delays (that is, discrete and infinite distributed delays) and Dirichlet boundary condition. First, using the Lyapunov–Krasoviskii functional scheme, the sufficient condition is obtained for the asymptotical synchronization of coupled semilinear diffusion PDEs with mixed time-delays and this condition is represented by linear matrix inequalities (LMIs), which is easy to be solved. Then the robust H∞synchronization is considered in temporal-spatial domain for the coupled semilinear diffusion PDEs with mixed delays and external disturbances. In terms of the technique of completing squares, the sufficient condition is obtained for the robust H∞synchronization. Finally, a numerical example of coupled semilinear diffusion PDEs with mixed time-delays is given to illustrate the correctness of the obtained results. Complexity 21: 42–53, 2016.