Output controllability of impulsive Boolean control networks based on hybrid-index model

In biological systems, impulses are often used to model mutations in gene expression. In order to describe the instantaneity of the impulse, this paper employs a hybrid-index model of impulsive Boolean networks with state-triggered impulses. Based on this model, the time-domain output controllability is investigated. Using the quotient mapping method, the hybrid-domain solutions of this model are mapped to the time-domain solutions, mathematically. Then a necessary and sufficient condition for output controllability in the time domain is presented. Finally, an example is given to demonstrate the correctness and effectiveness of the obtained results.