Input-state incidence matrix of Boolean control networks and its applications

The input-state incidence matrix of a control Boolean network is proposed. It is shown that this matrix contains complete information of the input-state mapping. Using it, an easily verifiable necessary and sufficient condition for the controllability of a Boolean control network is obtained. The corresponding control which drives a point to a given reachable point is designed. Moreover, certain topological properties such as the fixed points and cycles of a Boolean control network are investigated. Then, as another application, a sufficient condition for the observability is presented. Finally, the results are extended to mix-valued logical control systems.