Asymptotic Feedback Stabilization of Boolean Control Networks With Random Impulsive Disturbances

Based on the hybrid-index model, this article investigates the asymptotic feedback set stabilization of Boolean control networks (BCNs) with random impulsive disturbances. In this model, it is assumed that the sequence of intervals between adjacent impulsive instants is independent and identically distributed. This assumption ensures that the subsequence of solutions sampled at impulsive moments is a Markov chain. Based on this assumption and the semi-tensor product (STP), random impulsive BCNs (RI-BCNs) can be converted into impulsive-interval driven probabilistic BCNs (ID-PBCNs), and the input-state transition probability matrix (IS-TPM) is constructed, the calculations of convergent target set in the hybrid domain and the time domain are discussed, and the necessary and sufficient conditions for asymptotic feedback set stabilizability are obtained. On this basis, we propose a design algorithm of state feedback controllers to stabilize RI-BCNs asymptotically with respect to a target set by using state-space partition, which enables the system to converge to a given set with the least number of impulsive intervals. Finally, the effectiveness of the obtained results is verified by simulations.