IEEE Trans Cybern. 2016 Dec;46(12):3377-3387. doi: 10.1109/TCYB.2015.2505903. Epub 2015 Dec 22.
This paper considers the asymptotic and finite-time synchronization of drive-response memristive neural networks (MNNs) with time-varying delays. It is known that the parameters of MNNs are state-dependent, and hence the traditional robust control and analytical techniques cannot be directly applied. This difficulty is overcome by using the concept of Filippov solution. However, the special characteristics of MNNs may lead to unexpected parameter mismatch issue when different initial conditions are chosen. Based on a new robust control design, the mismatching issue is solved. Sufficient conditions are derived to guarantee the asymptotic synchronization of the considered MNNs with delays, which may be less conservative than synchronization criterion obtained by using existing methods. Moreover, without using the existing finite-time stability theorem, finite-time synchronization of the MNNs with delays is also investigated. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.
本文研究了时变时滞驱动响应忆阻神经网络（MNN）的渐近同步和有限时间同步。已知 MNN 的参数是状态相关的，因此传统的鲁棒控制和分析技术不能直接应用。通过使用 Filippov 解的概念克服了这一困难。然而，MNN 的特殊特性可能会导致选择不同的初始条件时出现意外的参数不匹配问题。基于新的鲁棒控制设计，解决了不匹配问题。得出了充分条件来保证具有时滞的所考虑的 MNN 的渐近同步，这可能比使用现有方法获得的同步准则更不保守。此外，无需使用现有的有限时间稳定性定理，也研究了具有时滞的 MNN 的有限时间同步。最后，提供了数值模拟来验证理论分析的有效性。
