IEEE Trans Neural Netw Learn Syst. 2015 Nov;26(11):2621-34. doi: 10.1109/TNNLS.2014.2387885. Epub 2015 Jan 20.
This paper investigates the stochastic synchronization problem for Markovian hybrid coupled neural networks with interval time-varying mode-delays and random coupling strengths. The coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric. A mode-dependent augmented Lyapunov-Krasovskii functional (LKF) is proposed, where some terms involving triple or quadruple integrals are considered, which makes the LKF matrices mode-dependent as much as possible. This gives significant improvement in the synchronization criteria, i.e., less conservative results can be obtained. In addition, by applying an extended Jensen's integral inequality and the properties of random variables, new delay-dependent synchronization criteria are derived. The obtained criteria depend not only on upper and lower bounds of mode-delays but also on mathematical expectations and variances of the random coupling strengths. Finally, two numerical examples are provided to demonstrate the feasibility of the proposed results.
本文研究了具有区间时变模态延迟和随机耦合强度的马尔可夫混合耦合神经网络的随机同步问题。耦合强度是相互独立的随机变量，并且耦合配置矩阵是非对称的。提出了一个模态相关的增广 Lyapunov-Krasovskii 泛函（LKF），其中考虑了一些涉及三或四元积分的项，这使得 LKF 矩阵尽可能模态相关。这在同步准则中带来了显著的改进，即可以得到更少保守的结果。此外，通过应用扩展 Jensen 积分不等式和随机变量的性质，推导出了新的时滞相关同步准则。所得到的准则不仅取决于模态延迟的上下界，还取决于随机耦合强度的数学期望和方差。最后，提供了两个数值示例来验证所提出结果的可行性。
