Stabilization of Markovian Jump Boolean Control Networks via Sampled-Data Control

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.