Passivity and passification of memristive neural networks with leakage term and time-varying delays

Abstract

This paper investigates passivity and passification for memristive neural networks (MNNs) with both leakage and time-varying delays. MNNs are converted into traditional neural networks (NNs) by nonsmooth analysis, then sufficient conditions are derived to guarantee the passivity based on Lyapunov method. A novel Lyapunov–Krasovskii functional (LKF) is constructed without requiring all the symmetric matrices to be positive definite. The relaxed passivity criteria with less conservativeness or complexity are obtained in the form of linear matrix inequalities (LMIs), which can be verified easily by the LMI toolbox. Then, the passification controller is designed with the relaxed criteria to ensure that MNNs with both leakage and time-varying delays are passive. Finally, two pertinent examples are presented to show the effectiveness of the theoretical results.