Delayed State-Flipped Control for Stabilization of Boolean Networks with Time Delays

This paper addresses the stabilization problem in Boolean networks with time delays (TBNs) under state-flipped control. First, the algebraic form of TBNs under state-flipped control is derived utilizing the semi-tensor product (STP) of matrices. Based on their periodic properties, the TBNs are then partitioned into subsystems. Subsequently, leveraging these developments, the equivalence between the stabilization of the original TBNs and that of the derived subsystems under state-flipped control is established. Furthermore, an equivalent stabilization criterion for the TBNs under state-flipped control is provided. An algorithm is also presented for constructing a flipped-set sequence to achieve stabilization. Finally, illustrative examples are provided to demonstrate the effectiveness of the theoretical results.