A New Estimation Method for Time–Space Sampled-Data Synchronization of RDNNs With Random Delays

The asymptotical synchronization in mean square of reaction–diffusion neural networks (RDNNs) with random delays is studied in this article. By sampling on both the time domain and spatial domain, a time–space sampled-data controller (TSSDC) is designed, which can efficiently save the network communication resources for RDNNs. A new processing method for the TSSDC is provided. Compared with the existing methods, the processing method here can capture more sampling information and is more concise. An extended Poincaré–Wirtinger inequality is proposed, which is in matrix form and less conservative. Then by constructing a sampling-dependent LKF, using the extended Poincaré–Wirtinger inequality and Hölder inequality, new mean square asymptotical synchronization criteria are set up for RDNNs with random delays, and the desired TSSDC gain is obtained. At length, a numerical example is given to verify the effectiveness and superiority of the obtained results.