College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, Xinjiang, China.
College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, Xinjiang, China.
Neural Netw. 2018 May;101:33-46. doi: 10.1016/j.neunet.2018.01.015. Epub 2018 Feb 8.
This paper considers the delay-dependent stability of memristive complex-valued neural networks (MCVNNs). A novel linear mapping function is presented to transform the complex-valued system into the real-valued system. Under such mapping function, both continuous-time and discrete-time MCVNNs are analyzed in this paper. Firstly, when activation functions are continuous but not Lipschitz continuous, an extended matrix inequality is proved to ensure the stability of continuous-time MCVNNs. Furthermore, if activation functions are discontinuous, a discontinuous adaptive controller is designed to acquire its stability by applying Lyapunov-Krasovskii functionals. Secondly, compared with techniques in continuous-time MCVNNs, the Halanay-type inequality and comparison principle are firstly used to exploit the dynamical behaviors of discrete-time MCVNNs. Finally, the effectiveness of theoretical results is illustrated through numerical examples.
本文研究了忆阻复值神经网络（MCVNNs）的时滞相关稳定性。提出了一种新的线性映射函数，将复值系统转化为实值系统。在这种映射函数下，本文分析了连续时间和离散时间 MCVNNs。首先，当激活函数连续但非 Lipschitz 连续时，证明了一个扩展矩阵不等式，以确保连续时间 MCVNNs 的稳定性。此外，如果激活函数不连续，通过应用 Lyapunov-Krasovskii 泛函设计一个不连续自适应控制器来获得其稳定性。其次，与连续时间 MCVNNs 的技术相比，首次使用 Halanay 型不等式和比较原理来研究离散时间 MCVNNs 的动态行为。最后，通过数值例子说明了理论结果的有效性。
