Multiple <i>μ</i>-Stable Synchronization Control for Coupled Memristive Neural Networks With Unbounded Time Delays
Libiao Peng, Xifeng Li, Dongjie Bi, Xuan Xie, Yongle Xie
Abstract
In this article, the multisynchronization issue of coupled memristive neural networks (CMNNs) with unbounded time delays is investigated. To begin with, a class of generalized Gaussian-wavelet-type activation functions is adopted to extend the number of stable equilibrium states. On this basis, a distributed impulsive controller is constructed to realize the multiple synchronization of the delayed CMNNs. Under the concepts of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> -stability, Filippov solution, and differential inclusion, some sufficient conditions are derived such that the addressed system can possess <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(2r + 1)^{n}\,\,\mu $ </tex-math></inline-formula> -stable synchronization manifolds. The convergence performance of solutions is determined by the time delays. As the time delays increase, the stability of synchronization manifolds will transform from exponential stability to power-stability, log-stability, or log–log-stability as special cases. Moreover, considering the modeling error and external disturbance, we further investigated the multisynchronization of delayed CMNNs with parametric uncertainties and stochastic perturbations, and some robust multisynchronization criteria are obtained. Finally, the effectiveness of the obtained results is verified by numerical simulations.