In this article, we study the finite-time stabilization and the asymptotic stabilization with probability one of Markovian jump Boolean control networks (MJBCNs) by sampled-data state feedback controls (SDSFCs). Based on the semi-tensor product (STP), we introduce an augmented variable multiplied by the vector form of the switching signal and the state of MJBCN. We find that under SDSFC, the sequence of the states of the augmented variable at sampling instants satisfies the Markov property. Based on the convergences of the switching signal and the augmented variable, we obtain the sufficient and necessary criteria for the finite-time stabilization and the asymptotic stabilization of MJBCNs by SDSFCs, respectively. Moreover, for the two kinds of stabilization, the feedback matrices of SDSFCs are constructed, respectively. Finally, the obtained results are applied to an apoptosis network and a model of the lactose operon in the Escherichia Coli.

中文翻译：

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通过采样数据控制稳定马尔可夫跳跃布尔控制网络。

在本文中，我们通过采样数据状态反馈控制（SDSFCs）研究了马尔可夫跳跃布尔控制网络（MJBCNs）的有限时间稳定和概率一的渐近稳定。基于半张量积（STP），我们引入了一个增广变量乘以开关信号的向量形式和MJBCN的状态。我们发现，在 SDSFC 下，增广变量在采样时刻的状态序列满足马尔可夫性质。基于开关信号和增广变量的收敛性，我们分别获得了SDSFCs对MJBCNs的有限时间稳定和渐近稳定的充分和必要标准。此外，对于这两种稳定，分别构建了SDSFC的反馈矩阵。最后，