A direct analysis method to Lagrangian global exponential stability for quaternion memristive neural networks with mixed delays

This paper mainly studies the global exponential stability in Lagrange sense (GESLS) of quaternion memristive neural networks (QMNNs) with leakage delays, unbounded dis-tributed delays and time-varying discrete time delays. In the process of research, instead of traditional decomposition into real-valued memristive neural networks (RMNNs) or complex-valued memristive neural networks (CMNNs), we consider the QMNN as a whole, and then give a sufficient condition related to time delays to ensure that the considered QMNN is GESLS. An example is provided to illustrate validity of theoretical results obtained in the end. The method proposed in the present text has two merits: (1) According to the definition of GESLS directly, no Lyapunov-Krasovskii functional (LKF) is required, which avoids massive calculations and solutions of high-dimensional matrix inequalities; (2) It is available not only to QMNNs, but also to RMNNs and CMNNs. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper focuses on the global exponential stability in Lagrange sense (GESLS) of quaternion memristive neural networks (QMNNs) with leakage delays, unbounded distributed delays, and time-varying discrete time delays. Instead of decomposing the QMNN into real-valued memristive neural networks (RMNNs) or complex-valued memristive neural networks (CMNNs), the paper considers the QMNN as a whole and provides a sufficient condition related to time delays to ensure GESLS. The proposed method has the advantages of not requiring Lyapunov-Krasovskii functional (LKF) and being applicable to different types of memristive neural networks.