Stabilization and set stabilization of delayed Boolean control networks based on trajectory stabilization

Using the algebraic state space representation method, this paper investigates the stabilization and set stabilization of delayed Boolean control networks (DBCNs). Firstly, the stabilization problem of DBCNs is formulated, which is proved to be equivalent to the trajectory stabilization of DBCNs. Secondly, based on the algebraic form of DBCNs, a necessary and sufficient condition is presented for the trajectory stabilization of DBCNs, which can also solve the stabilization problem. A constructive procedure is proposed for the design of state feedback stabilizers of DBCNs. Thirdly, the set stabilization problem and partial stabilization problem of DBCNs are studied, and several necessary and sufficient conditions are presented. Finally, the obtained results are applied to the strategy consensus of networked evolutionary games with memories.