Finite-Time Synchronization of Fractional-Order Quaternion-Valued Delayed Cohen-Grossberg Neural Networks

The finite-time synchronization (FTS) is investigated in this paper for delayed fractional-order quaternion-valued Cohen-Grossberg neural networks (FQVCGNNs). First, a fractional-order finite-time stability theorem is established by using the definition of fractional-order integral and reduction to absurdity. Next, two novel quaternion-valued feedback controller and quaternion-valued adaptive controller are designed respectively to achieve the FTS of FQVCGNNs. Then, without the participation of sign function, applying the non-decomposition method, the established finite-time stability theorem and constructing suitable quaternion-valued Lyapunov function, some less conservative and easily verifiable criteria are presented to ensure the FTS of the addressed system. Meanwhile, the settling time of FTS is effectively estimated, which depends on the controller parameters and the fractional order of the considered system. Finally, two numerical examples are provided to show the validity of the obtained results.