Global mittag-leffler synchronization of fractional-order neural networks with time-varying delay via hybrid sliding mode control

Abstract

In this paper, the global Mittag-Leffler synchronization (GMLS) for fractional-order neural networks with time-varying delay (FNNTVD) is studied based on hybrid sliding mode control (HSMC). First, a class of sliding surface is designed to study the dynamic behavior of FNNTVD by using the integer order Lyapunov direct method, which resolves the problem that the activation function of FNNTVD cannot be applied to the construction of Lyapunov function in the previous literature. Then, a new HSMC with the fixed signal transmission time delay is developed to ensure GMLS of FNNTVD. Next, based on Lyapunov direct method and the designed HSMC, some criteria are put forward to achieve GMLS of FNNTVD. Finally, two examples are given to verify the effectiveness of the proposed synchronization criteria for FNNTVD.