Stabilization of switched boolean control networks by state feedback

This paper investigates the stabilization of switched Boolean control networks (SBCNs) by using the semi-tensor product of matrices. First, the algebraic form of the switched Boolean control network based on the new product of matrices is presented, and the k-step controllability matrices and the controllability matrix are given, based on which a necessary and sufficient condition for stabilizability of SBCNs by state feedbacks and state-dependent switching laws is provided. Second, for a given SBCN, all the available feedback controllers and switching sequences which stabilize the system in the shortest time are obtained. At last, an example is provided to illustrate the main results obtained in this paper.