IEEE Trans Neural Netw Learn Syst. 2022 Aug;33(8):3829-3841. doi: 10.1109/TNNLS.2021.3054615. Epub 2022 Aug 3.
In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.
本文研究了具有时变时滞的随机马尔可夫跳跃神经网络（SMJNN）在非周期采样数据控制下的采样数据同步问题。通过构造模态相关单边环基李雅普诺夫泛函和模态相关双边环基李雅普诺夫泛函，并利用伊藤公式，提出了两种不同的基于非周期采样数据的误差 SMJNN 随机稳定性准则。根据所提出的随机稳定性条件，可以保证从系统与主系统同步。此外，还分别基于这两个不同的随机稳定性准则，提出了两种用于误差 SMJNN 的模态相关非周期采样数据控制器设计方法。最后，通过两个数值模拟示例验证了本文给出的非周期采样数据控制器的设计方法可以有效地稳定不稳定的 SMJNN。还表明，模态相关双边环函数方法比模态相关单边环函数方法给出的结果更不保守。
