School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China.
Texas A & M University at Qatar, PO Box 23874, Doha, Qatar.
Neural Netw. 2019 Oct;118:289-299. doi: 10.1016/j.neunet.2019.07.006. Epub 2019 Jul 15.
The Lyapunov-Krasovskii functional approach is an important and effective delay-dependent stability analysis method for integer order system. However, it cannot be applied directly to fractional-order (FO) systems. To obtain delay-dependent stability and stabilization conditions of FO delayed systems remains a challenging task. This paper addresses the delay-dependent stability and the stabilization of a class of FO memristive neural networks with time-varying delay. By employing the FO Razumikhin theorem and linear matrix inequalities (LMI), a delay-dependent asymptotic stability condition in the form of LMI is established and used to design a stabilizing state-feedback controller. The results address both the effects of the delay and the FO. In addition, the upper bound of the absolute value of the memristive synaptic weights used in previous studies are released, leading to less conservative conditions. Three numerical simulations illustrate the theoretical results and show their effectiveness.
李雅普诺夫-克拉索夫斯基泛函方法是一种重要且有效的整数阶系统时滞相关稳定性分析方法。然而，它不能直接应用于分数阶（FO）系统。因此，获得 FO 时滞系统的时滞相关稳定性和镇定条件仍然是一个具有挑战性的任务。本文针对一类具有时变时滞的 FO 忆阻神经网络，研究了其时滞相关稳定性和镇定问题。通过 FO Razumikhin 定理和线性矩阵不等式（LMI），建立了一种时滞相关渐近稳定条件的 LMI 形式，并用于设计一种稳定的状态反馈控制器。该结果同时考虑了时滞和 FO 的影响。此外，还放宽了之前研究中使用的忆阻突触权重的绝对值的上界，得到了更为保守的条件。三个数值模拟说明了理论结果的有效性。
