Perturbation analysis for reachability and controllability of probabilistic Boolean control networks based on the semi-tensor product

This paper investigates the influence of function perturbation on the reachability and controllability of probabilistic Boolean control networks (PBCNs) using the algebraic framework based on the semi-tensor product (STP) of matrices. The influence of perturbation on the reachability and controllability of PBCNs is classified into four cases according to whether the perturbed control can substitute the original one. For each case, a reachability perturbation matrix is constructed to demonstrate the changes in the reachability matrix caused by function perturbation. Based on this, some results of the perturbation analysis on the reachability and controllability of PBCNs are presented.