This paper studies the set stabilization of Boolean control networks (BCNs) under sampled-data state feedback control (SDSFC). The main research content is divided into two parts. First, the topological structure of BCNs under given SDSFC is investigated. The fixed point and sampled cycle are defined, respectively. It is found that sampled cycles allow elements to be repeated and not every element can be regarded as an initial state, and this is quite different from conventional cycles of BCNs. A theorem is presented to calculate the number of fixed points and an algorithm is given to find all fixed points and sampled cycles. Second, the set stabilization problem of BCNs by SDSFC is investigated based on the sampled point set and the sampled point control invariant set (SPCIS). A necessary and sufficient condition is derived for the global set stabilization of BCNs by SDSFC, and further sampled-data state feedback controllers are also designed. The interesting thing is that if a state enters the SPCIS as an unsampled point, then it may run out of the given set again, which is in sharp contrast to conventional BCNs. Finally, an example is given to illustrate the efficiency of the obtained results.

中文翻译：

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布尔控制网络集合稳定的采样数据状态反馈控制

本文研究了采样数据状态反馈控制 (SDSFC) 下布尔控制网络 (BCN) 的集合稳定性。主要研究内容分为两部分。首先，研究了给定 SDSFC 下 BCN 的拓扑结构。分别定义了定点和采样周期。发现采样循环允许元素重复，而不是每个元素都可以视为初始状态，这与传统的 BCN 循环有很大不同。提出了一个定理来计算不动点的数量，并给出一个算法来找到所有不动点和采样周期。其次，基于采样点集和采样点控制不变集（SPCIS）研究了 SDSFC 的 BCN 集镇定问题。SDSFC 推导出 BCN 全局集稳定的充分必要条件，并且还设计了进一步的采样数据状态反馈控制器。有趣的是，如果一个状态作为未采样点进入 SPCIS，那么它可能会再次耗尽给定的集合，这与传统的 BCN 形成鲜明对比。最后给出一个例子来说明所得结果的有效性。