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.

Automated summary

This paper discusses the asymptotical synchronization and the input-to-state exponential stability of multi-layer networks based on memristors with delays under coupling disturbance and stochastic noise. Differential inclusion and Laplace transform methods are used to address the nonlinear coupling function and discontinuous activation. New sufficient conditions based on Lyapunov-Krasovskii functional, inequality technique, and linear matrix inequality are derived to ensure the stability of the considered model. Two examples and simulations are provided to illustrate the validity and correctness of the conclusions.