State feedback controller design for synchronization of master-slave Boolean networks based on core input-state cycles

Core input-state cycles are proposed to investigate the synchronization of two deterministic Boolean networks coupled in the master-slave configuration. Firstly, by using the algebraic form of the master-slave system, a new Boolean control network (BCN) is constructed and an algorithm is given to find core input-state cycles of the newly constructed BCN. Secondly, based on these cycles, a necessary and sufficient condition is derived for the existence of a synchronizing state feedback controller. Accordingly, an algorithm is provided for verifying the existence of feasible state feedback controllers. Thirdly, a constructive method is developed to design a synchronizing state feedback controller when the existence condition obtained above is satisfied. Our results are significantly superior to the existing relevant results. Finally, an example is employed to show the effectiveness of our results.