Stabilization of Boolean control networks with state-triggered impulses

Previously, impulses were used to model abrupt changes in dynamic biological systems. This paper introduces a hybrid-index model that can characterize instantaneity of the impulsive behavior more effectively, compared with the existing impulsive Boolean network models. Using the hybrid-index model, we investigate the set stabilization of Boolean control networks with state-triggered impulses in the hybrid-domain and the time-domain. We establish necessary and sufficient conditions for set stabilizability in the hybrid and time domains, using the methods of k-domain and quotient mapping, respectively. Further, we obtain algorithms for constructing all hybrid-optimal and time-optimal set stabilizers by partitioning the state space into layers. The relationships between different set stabilizabilities are summarized. In addition, we have shared two examples to demonstrate the main results.