Chen Jun, Park Ju H, Xu Shengyuan
IEEE Trans Cybern. 2022 Nov;52(11):11885-11892. doi: 10.1109/TCYB.2021.3076196. Epub 2022 Oct 17.
This article investigates the stability problem for discrete-time neural networks with a time-varying delay by focusing on developing new Lyapunov-Krasovskii (L-K) functionals. A novel L-K functional is deliberately tailored from two aspects: 1) the quadratic term and 2) the single-summation term. When the variation of the discrete-time delay is further considered, the constant matrix involved in the quadratic term is extended to be a delay-dependent one. All these innovations make a contribution to a quadratic function with respect to the delay from the forward differences of L-K functionals. Consequently, tractable stability criteria are derived that are shown to be more relaxed than existing results via numerical examples.
本文通过专注于开发新的李雅普诺夫 - 克拉索夫斯基（L - K）泛函来研究具有时变延迟的离散时间神经网络的稳定性问题。一种新颖的L - K泛函从两个方面特意进行了定制：1）二次项；2）单重求和项。当进一步考虑离散时间延迟的变化时，二次项中涉及的常数矩阵扩展为与延迟相关的矩阵。所有这些创新为基于L - K泛函前向差分的延迟二次函数做出了贡献。因此，推导出了易于处理的稳定性准则，通过数值例子表明这些准则比现有结果更为宽松。
