Stability analysis for memristor-based stochastic multi-layer neural networks with coupling disturbance

This paper discusses the asymptotical synchronization and the input-to-state exponential stability for memrist or-based multi-layers networks with delays under the coupling disturbance and stochastic noise. First, in order to solve the nonlinear coupling function of mismatched parameter and discontinuous activation in the system, methods of differential inclusion and Laplace transform are used. Then, based on the Lyapunov–Krasovskii functional, technique of inequality and linear matrix inequality, new sufficient conditions are also derived, in order to ensure the asymptotic synchronization and the input-to-state exponential stability of the considered model. Finally, two examples and simulations are given to illustrate the validity and correctness of our conclusions. •The stability of stochastic multi-layer networks with disturbances is investigated.•It is more challenging and practical to study memristor-based stochastic systems.•Using LMIs and Lyapunov functional, sufficient conditions of stability are obtained.•The method in this paper can be applied to study other types of neural networks.