Adaptive exponential synchronization of memristive neural networks with mixed time-varying delays

Abstract

This study is focused on the issue of adaptive exponential synchronization for a general class of memristive neural networks (MNNs) with mixed time-varying delays. A new and simple adaptive controller with feedback control law is designed to achieve exponential synchronization by using Lyapunov functional method. The adaptive controller proposed in the paper possesses a powerful adaptive capability that it can be utilized for various MNNs with different mathematical definitions of memristor. In addition, no excessive calculations such as solving linear matrix inequality or computing algebraic conditions are required in our synchronization criteria. We also present two synchronization conditions for a special class of MNNs that part or even all of the system׳s right-hand is reduced to be continuous when activation functions are zero at the neuron׳s switching points. And two lemmas are introduced to modify a misunderstanding in this situation in some previous papers. Finally, an example with numerical simulations is presented to illustrate the efficiency and accuracy of the theoretical results.