Synchronizations control of fractional-order multidimension-valued memristive neural networks with delays

Abstract

In this paper, systems of the fractional-order multidimension-valued memristive neural networks (FMVMNNs) with leakage delay and time-varying delays are studied in continuous-time and discrete-time cases. Comparative studies on synchronizations control between discrete-time FMVMNNs and the continuous-time system are investigated directly rather than through the decomposition method. By employing Lyapunov theory and fractional derivative inequalities, sufficient criteria about the quasi-synchronization and global ultimate Mittag-Leffler lag quasi-synchronization are obtained in multidimension-valued linear matrix inequality form, while succinct conclusions of asymptotical synchronization and global Mittag-Leffler synchronization are derived in vector form. The obtained criteria have many advantages in a less computation, lower conservatism, more generality and higher flexibility. Finally, four examples are given to demonstrate the effectiveness and availability of the derived conclusions.