IEEE Trans Neural Netw Learn Syst. 2020 Feb;31(2):639-650. doi: 10.1109/TNNLS.2019.2908755. Epub 2019 Apr 23.
This paper is concerned with the problem of global exponential passivity for quaternion-valued memristor-based neural networks (QVMNNs) with time-varying delay. The QVMNNs can be seen as a switched system due to the memristor parameters are switching according to the states of the network. This is the first time that the global exponential passivity of QVMNNs with time-varying delay is investigated. By means of a nondecomposition method and structuring novel Lyapunov functional in form of quaternion self-conjugate matrices, the delay-dependent passivity criteria are derived in the forms of quaternion-valued linear matrix inequalities (LMIs) as well as complex-valued LMIs. Furthermore, the asymptotical stability criteria can be obtained from the proposed passivity criteria. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.
本文研究了时变时滞四元数值忆阻神经网络（QVMNNs）的全局指数被动性问题。由于忆阻器参数根据网络状态进行切换，因此 QVMNN 可以视为切换系统。这是首次研究具有时变时滞的 QVMNN 的全局指数被动性。通过非分解方法和构造新型的四元自共轭矩阵形式的李雅普诺夫泛函，以四元数线性矩阵不等式（LMIs）和复数 LMIs 的形式推导出了时滞相关的被动性判据。此外，可以从提出的被动性判据中得到渐近稳定性判据。最后，通过一个数值实例说明了理论结果的有效性。
