State-Feedback Set Stabilization of Boolean Networks With State-Dependent Random Impulses
研究了具有状态依赖随机脉冲的布尔控制网络的状态反馈集镇定问题，利用混合索引模型描述脉冲行为，提出了前向完备性判据和最大控制不变子集算法，给出了有限时间和渐近集镇定的充要条件。
In this article, we are devoted to addressing the state-feedback set stabilization of Boolean control networks with state-dependent random impulses by utilizing a hybrid index model. By comparison with the previous impulsive Boolean networks, this model can be used to describe the instantaneousness of various impulsive behaviors more clearly. In order to avoid the occurrence of Zeno phenomenon, we first introduce the basic concept of forward completeness and further establish the judging criterion. After that, an algorithm is presented to derive the largest control invariant subset of a given subset. Based on this, we derive a necessary and sufficient criterion for finite-time feedback set stabilizability. Similarly, the result is also obtained for the asymptotic case, and the asymptotic set stabilizers are designed by dividing the whole state space into several layers. Moreover, we also investigate the relationships between different stabilizabilities. Last, two illustrative examples are presented to demonstrate the efficiency of the theoretical results.