Weak reachability of probabilistic boolean control networks

This paper concerns the weak reachability of probabilistic Boolean control networks (PBCNs). Using semi-tensor product, PBCNs are expressed as discrete time bilinear systems with respect to states and controls. From the algebraic form of PBCNs, the maximum transfer probability matrix for PBCNs is constructed. From the matrix, necessary and sufficient condition for weak reachability of PBCNs is given. Also, a numerical example is presented to show the applicability of our approach.