Global stability and controllability of switched Boolean networks

This paper investigates the global stability and controllability of switched Boolean networks (BNs) by using the semitensor product method. First, the model of switched Boolean networks is introduced and expressed into the algebraic form. Second, the concept of the switching reachability of points for switched BNs is defined and a necessary and sufficient condition is presented to verify the switching reachability of points by constructing the switching-state incidence matrix. Third, a necessary and sufficient condition is proposed to check the global stability of switched BNs under arbitrary switching signals by using the switching reachability of points. Finally, the concept of the controllability for switched Boolean control networks is given, and several necessary and sufficient conditions are obtained for the controllability. The study of two illustrative examples shows that the new results obtained in this paper are very effective in investigating the global stability and controllability of switched BNs.