This article investigates the set stabilization of impulsive Boolean control networks (IBCNs) by sampled-data state feedback control based on a hybrid index model. It is worth mentioning that the 2-D index model has the ability to characterize the instantaneousness of ideal impulses and describe complicated impulsive behaviors. To avoid Zeno phenomenon, the judging conditions for forward completeness are derived. Subsequently, an algorithm is designed to obtain the largest sampled point control invariant set (SPCIS) of a given set in the hybrid domain, and its validity is further authenticated. Accordingly, a necessary and sufficient condition is derived for the set stabilization of IBCNs in the hybrid domain, and all time-optimal sampled-data state feedback controllers are designed. The similar results are also obtained for IBCNs in the time domain. Compared with set stabilization in the time domain, set stabilization in the hybrid domain not only focuses on the dynamics at each time instant but also concerns every jumping state. It results in that every SPCIS in the hybrid domain is a subset of a certain SPCIS in the time domain. Eventually, the $\lambda$ switch with impulsive disturbances is modeled as a reduced IBCN, which is presented to demonstrate the obtained results.

中文翻译：

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基于混合索引模型的脉冲布尔网络的采样数据集镇定

本文研究基于混合索引模型的采样数据状态反馈控制的脉冲布尔控制网络（IBCN）的集合稳定性。值得一提的是，二维索引模型具有表征理想脉冲的瞬时性并描述复杂的脉冲行为的能力。为了避免芝诺现象，推导了前向完整性的判断条件。随后，设计一种算法以获得混合域中给定集合的最大采样点控制不变集合（SPCIS），并进一步验证其有效性。因此，为混合域中的IBCN的集合稳定性导出了一个充要条件，并设计了所有时间最优的采样数据状态反馈控制器。对于IBCN，在时域中也获得了类似的结果。与时域中的集合稳定相比，混合域中的集合稳定不仅关注每个时刻的动态，而且还涉及每个跳跃状态。结果是，混合域中的每个SPCIS都是时域中某个SPCIS的子集。最终，$ \ lambda $ 带有脉冲干扰的开关被建模为简化的IBCN，用于证明所获得的结果。