A novel fixed-time stability theorem with application to synchronization in switched coupled neural networks

This paper investigates fixed-time (FXT) synchronization in switched coupled neural networks (SCNNs) building on an improved FXT stability theorem. First, the FXT stability criterion and the settling time (ST) are enhanced by employing the method of reduction to absurdity. As a key application, FXT synchronization is developed for SCNNs with both discontinuous and continuous activation functions. By designing a discontinuous controller incorporating switched signals and employing the theory of differential inclusions, several criteria are established to guarantee FXT synchronization in the considered networks. Ultimately, two numerical illustrations are provided to showcase the efficacy and correctness of the theoretical findings.