Stability Criteria of Delayed Memristor-Based Neural Networks via Continuous-Time Model and Interval Matrix Approach

Abstract

Modeling and stability analysis of memristor-based neural networks (MNNs) are the premise of designs and applications. Different from most previous research, delayed MNNs are described by continuous differential equations with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{2n^{2}+n}$</tex-math> </inline-formula> variables where the memductances of memristors are continuously dependent on the fluxes. Both system delays and input delays are considered, and the delays and their derivatives may vary in intervals whose lower bounds are not restricted to be zero. The systems are further reduced to continuous-time neural networks (NNs) with interval matrix uncertainties, and a unified method is developed to solve the stability of delayed NNs and MNNs. Stability criteria are obtained for delayed MNNs by augmented Lyapunov functionals, Wirtinger-based integral inequality, reciprocally convex approach, and linear matrix inequalities. In the end, two numerical simulations are used to demonstrate the validity of our theorems.