Output synchronisation design for master-slave Boolean networks

The output synchronisation of two deterministic Boolean networks coupled in the master-slave configuration is studied. First, under the algebraic framework of logical systems, an auxiliary system is constructed. Second, core input-state cycles are generalised and an algorithm is given to calculate these cycles. Third, based on core input-state cycles of the newly constructed auxiliary system, a necessary and sufficient existence condition is derived for a synchronising state feedback controller. Furthermore, a constructive method is provided to get feasible state feedback controllers when the existence condition obtained above is satisfied. Finally, an illustrative example is provided to verify the effectiveness and superiority of the presented results.