Exponential synchronization of master-slave neural networks with time-delays

This paper establishes an exponential H∞ synchronization method for a class of master and slave neural networks (MSNNs) with mixed time-delays, where the delays comprise different neutral, discrete and distributed time-delays and the class covers the Lipschitz-type nonlinearity case. By introducing a novel discretized Lyapunov-Krasovskii functional in order to minimize the conservatism in the stability problem of the system and also using some free weighting matrices, new delay-dependent sufficient conditions are derived for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities (LMIs). The controller guarantees the exponential H∞ synchronization of the two coupled MSNNs regardless of their initial states. Detailed comparisons with different number of segments are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.