Controllability and stabilizability of probabilistic logical control networks

Necessary and sufficient conditions of controllability and stabilizability of probabilistic Boolean control networks are first introduced, by using the controllability matrix of switched Boolean control networks. Then, these results are generalized to mix-valued logical control networks, which include the Boolean control networks as a special case. The algebraic forms of mix-valued logical control networks and Boolean networks make this generalization very natural. Finally, using the input-state incidence matrix of higher-order logical control networks, the results are also extended to higher-order case.