IEEE Trans Cybern. 2022 Oct;52(10):10290-10301. doi: 10.1109/TCYB.2021.3069750. Epub 2022 Sep 19.
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.
在本文中，我们通过采样数据状态反馈控制（SDSFC）研究马尔可夫跳变布尔控制网络（MJBCN）的有限时间稳定和概率一渐近稳定。基于张量积（STP），我们引入了一个增广变量，该变量乘以切换信号和 MJBCN 状态的向量形式。我们发现，在 SDSFC 下，在采样时刻增广变量的状态序列满足马尔可夫性质。基于切换信号和增广变量的收敛性，我们分别获得了 SDSFC 对 MJBCN 的有限时间稳定和渐近稳定的充分必要条件。此外，对于这两种稳定，分别构建了 SDSFC 的反馈矩阵。最后，将所得到的结果应用于细胞凋亡网络和大肠杆菌乳糖操纵子的模型。
