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

• Compared with the usual methods, the direct analysis method proposed in the paper can not only derive simple solvable conditions, but also need not construct any LKF. • The proposed method is applicable to both RMNNs and CMNNs. • No model transformation is involved, which reduces the derivation process. This paper mainly studies 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. 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. [ABSTRACT FROM AUTHOR]