IEEE Trans Neural Netw Learn Syst. 2018 Apr;29(4):856-868. doi: 10.1109/TNNLS.2017.2651023. Epub 2017 Jan 25.
In this paper, a general class of delayed memristive neural networks (DMNNs) system described by functional differential equation with discontinuous right-hand side is considered. Under the extended Filippov-framework, we investigate the finite-time stabilization problem for DMNNs by using the famous finite-time stability theorem and the generalized Lyapunov functional method. To do so, we design two classes of novel controllers including discontinuous state-feedback controller and discontinuous adaptive controller. Without assuming the boundedness and monotonicity of the activation functions, several sufficient conditions are given to stabilize the states of this class of DMNNs in finite time. Moreover, the upper bounds of the settling time for stabilization are estimated. Finally, numerical examples are provided to demonstrate the effectiveness of the developed method and the theoretical results.
本文研究了一类具有间断右端的泛函微分方程描述的广义时滞忆阻神经网络（DMNN）系统。在扩展的 Filippov 框架下，利用著名的有限时间稳定性定理和广义 Lyapunov 函数方法，研究了 DMNN 的有限时间稳定化问题。为此，设计了两类新型控制器，包括不连续状态反馈控制器和不连续自适应控制器。在不假设激活函数有界和单调的情况下，给出了几个充分条件，以有限时间稳定该类 DMNN 的状态。此外，还估计了稳定的调整时间上限。最后，通过数值例子验证了所提出方法和理论结果的有效性。
