LAUSR

Abstract The issue of finite-time synchronization (FTS) of discontinuous reaction-diffusion neural networks (DRDNNs) with time-varying coefficients is investigated here. First, the effects caused by discontinuous activations are handled by differential inclusion theory. Secondly, a relaxed Lyapunov function (RLF) method is introduced to design novel control algorithms, including state-feedback control and adaptive control, to achieve FTS of DRDNNs, and the upper-bound of the settling time is explicitly estimated. In this RLF method, the LF is allowed to be nonsmooth and possess an indefinite derivative. Moreover, the FTS results via generalized pinning state-feedback and generalized pinning adaptive control are presented as two corollaries. Finally, two numerical simulations are presented to substantiate the merits of the obtained results.