Spacial sampled-data control for H∞ output synchronization of directed coupled reaction–diffusion neural networks with mixed delays

Abstract This work investigates the H ∞ output synchronization (HOS) of the directed coupled reaction–diffusion (R-D) neural networks (NNs) with mixed delays. Firstly, a model of the directed state coupled R-D NNs is introduced, which not only contains some discrete and distributed time delays, but also obeys a mixed Dirichlet–Neumann boundary condition. Secondly, a spacial sampled-data controller is proposed to achieve the HOS of the considered networks. This type of controller can reduce the update rate in the process of control by measuring the state of networks at some fixed sampling points in the space region. Moreover, some criteria for the HOS are established by designing a appropriate Lyapunov functional, and some quantitative relations between diffusion coefficients, mixed delays, coupling strength and control parameters are given accurately by these criteria. Thirdly, the case of directed spatial diffusion coupled networks is also studied and, the following finding is obtained: the spatial diffusion coupling can suppress the HOS while the state coupling can promote it. Finally, one example is simulated as the verification of the theoretical results.