This paper mainly studies the problem of global stability at limit cycles for switched multi‐valued logical networks (SMLNs). Firstly, the SMLNs are converted into algebraic forms by using semi‐tensor product of matrices. Then an effective method called digital transformation is used to analyze the structural matrices of the obtained algebraic equations. Based on this method, the global stability at a certain limit cycle for SMLNs, a more general situation, is for the first time studied in this paper, and the relevant necessary and sufficient condition is derived. By dividing the structural matrices of switched multi‐valued logical control networks (SMLCNs) into several blocks, a necessary and sufficient condition for SMLCNs to be globally stabilized to a limit cycle under open‐loop control signals is provided. In addition, due to the use of digital transformations, the stability analysis method established for SMLNs and SMLCNs in this paper is sraightforward and the corresponding computational burden is quite small. Finally, two numerical examples are given to show the effectiveness of the obtained results in this work.

中文翻译：

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交换式多值逻辑网络在极限周期内的全局稳定性

本文主要研究交换多值逻辑网络（SMLN）在极限环上的全局稳定性问题。首先，通过使用矩阵的半张量积将SMLN转换为代数形式。然后使用一种称为数字变换的有效方法来分析所获得的代数方程的结构矩阵。基于此方法，本文首次研究了SMLNs在一定极限环上的全局稳定性，这是一个更为普遍的情况，并推导了相关的充要条件。通过将交换式多值逻辑控制网络（SMLCN）的结构矩阵划分为几个块，为在开环控制信号下SMLCN全局稳定到极限循环提供了充要条件。此外，由于采用了数字变换，本文建立的针对SMLN和SMLCN的稳定性分析方法比较简单，相应的计算量也很小。最后，给出了两个数值例子来说明所获得的结果在这项工作中的有效性。