Controllability and Observability of Singular Boolean Control Networks

Controllability and observability of singular Boolean control networks are proposed in this paper from its algebraic form via semi-tensor product. First, the input-state incidence matrix of singular Boolean control networks is presented based on which the generalized input-state incidence matrix is also defined. Second, a necessary and sufficient condition for the controllability of singular Boolean control networks is given, as well as an algorithm to design controls which drive a state to a reachable state. At last, similar to Boolean control networks, a sufficient condition of observability of singular Boolean control networks is obtained.