PD control for passivity of coupled reaction-diffusion neural networks with multiple state couplings or spatial diffusion couplings

This paper studies the passivity for coupled reaction-diffusion neural networks with multiple state couplings (CRDNNMSCs) or spatial diffusion couplings (CRDNNMSDCs) by employing the proportional-derivative (PD) control method. Firstly, a PD control strategy is presented for the sake of ensuring the passivity of CRDNNMSCs, and a synchronization condition is also given by utilizing the output-strict passivity of CRDNNMSCs. In addition, some corresponding conditions for guaranteeing the passivity and synchronization of CRDNNMSDCs are also developed in virtue of PD controller. Lastly, the correctness of the obtained passivity and synchronization criteria for the proposed models is verified by two numerical examples.