Stability analysis of memristor-based complex-valued recurrent neural networks with time delays

This article addresses stability analysis of a general class of memristor-based complex-valued recurrent neural networks (MCVNNs) with time delays. Some sufficient conditions to guarantee the boundedness on a compact set that globally attracts all trajectories of the MCVNNs are obtained by utilizing local inhibition. Moreover, some sufficient conditions for exponential stability and the global stability of the MCVNNs are established with the help of local invariant sets and linear matrix inequalities using Lyapunov-Krasovskii functional. The analysis results in the article, based on the results from the theory of differential equations with discontinuous right-hand sides as introduced by Filippov. Finally, two numerical examples are also presented to show the effectiveness and usefulness of our theoretical results.