Stability analysis of stochastic Lyapunov functions: Applications to memristor neural networks

Abstract

This paper investigates the mean square exponential stability of stochastic neural networks relying on memristor with leakage delay with different types of activation functions. To this aim, we introduce a new suitable stochastic Lyapunov-Krasovskii functional (SLKF) and employ Filippov solutions to derive stability criteria using It $\hat{o}$'s formula. We encounter with a nonlinear matrix inequality which should be converted to a linear matrix inequality (LMI) problem by using Schur complement lemma. The proposed problem is handled by using the CVX toolbox in MATLAB software. In the numerical examples section, we bring two examples related to two- and three-dimentional memristor-based neural networks whose coefficients satisfy in the Schur complement lemma. The figures show that the employed stochastic Lyapunov functions can capture the exponential stability conditions.