This article is concerned with the local stabilization of memristive neural networks subject to actuator saturation via aperiodic sampled-data control. A dynamic partitioning point is elegantly introduced, which is placed between the latest sampling instant and the present time to utilize more information of the inner sampling. To analyze the stability of the closed-loop system, a time-dependent two-side looped functional, which fully utilizes the state information on the entire sampling interval as well as at the dynamic partitioning point, is constructed. It relaxes the positive definiteness of traditional Lyapunov functional inside the sampling interval and therefore, provides the possibility to derive less conservative stability results. Besides, an auxiliary system is established to describe the dynamics at the partitioning point. On the basis of the constructed looped functional, the discrete-time Lyapunov theorem, and some estimation approaches, a linear matrix inequalities-based stability criterion is developed, and then, the sampled-data saturated controller is designed to ensure the local asymptotic stability of the closed-loop system. Thereafter, two optimization problems are developed to seek the desired feedback gain and to expand the estimation of the region of attraction or to enlarge the upper bound of the sampling interval. Eventually, a numerical example is given to demonstrate the effectiveness and the superiority of the proposed results.

中文翻译：

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具有执行器饱和的忆阻神经网络稳定的非周期采样数据控制：一种动态分区方法

本文关注的是通过非周期性采样数据控制使受执行器饱和影响的忆阻神经网络的局部稳定性。优雅地引入了动态分区点，将其放置在最新采样时刻和当前时间之间，以利用内部采样的更多信息。为了分析闭环系统的稳定性，构建了一个充分利用整个采样区间以及动态分割点的状态信息的时间相关的两侧循环泛函。它放宽了采样区间内传统 Lyapunov 函数的正定性，因此提供了获得不太保守的稳定性结果的可能性。此外，还建立了一个辅助系统来描述分区点的动态。基于构造的循环泛函、离散时间李亚普诺夫定理和一些估计方法，开发了基于线性矩阵不等式的稳定性准则，然后设计了采样数据饱和控制器以确保局部渐近稳定性闭环系统。此后，开发了两个优化问题来寻求所需的反馈增益并扩大吸引区域的估计或扩大采样间隔的上限。最后，给出了一个数值例子来证明所提结果的有效性和优越性。采样数据饱和控制器的设计保证了闭环系统的局部渐近稳定性。此后，开发了两个优化问题来寻求所需的反馈增益并扩大吸引区域的估计或扩大采样间隔的上限。最后，给出了一个数值例子来证明所提结果的有效性和优越性。采样数据饱和控制器的设计保证了闭环系统的局部渐近稳定性。此后，开发了两个优化问题来寻求所需的反馈增益并扩大吸引区域的估计或扩大采样间隔的上限。最后，给出了一个数值例子来证明所提结果的有效性和优越性。