Finite-Time Synchronization of Discontinuous Fractional-Order Multi-Layer Coupled Neural Networks via Aperiodic Intermittent Control

This paper is mainly concentrated on finite-time synchronization (FTS) for discontinuous fractional-order multi-layer coupled neural networks (FMCNNs) under aperiodic intermittent control. The discontinuous activation function is introduced to capture abrupt transitions and switching phenomena widely observed in practical neural dynamics. However, such nonsmooth behaviors significantly increase the complexity of controller design and synchronization analysis. To cope with these problems, an aperiodic intermittent controller with a simple structure is developed within the Filippov differential inclusion framework, ensuring effective handling of nonsmooth neural dynamics while reducing control cost. More importantly, a piecewise fractional-order differential inequality is established to characterize the evolution of the Lyapunov function over the control and rest intervals under aperiodic switching. This inequality serves as a fundamental analytical tool for deriving sufficient conditions for FTS and estimating the settling time. Compared with the existing results, the proposed framework relaxes the restrictions on the power exponent and provides a more general analytical tool for investigating the FTS of discontinuous FMLCNNs. In the end, a simulation example is provided to show the validity of the proposed method.