Controllability and observability of switched Boolean control networks

The controllability and observability are investigated for a class of switched Boolean control networks (SBCNs). Using semi-tensor product of matrices, the dynamics of an SBCN can be transformed into an algebraic form. The model-input-state (MIS) matrix of an SBCN is introduced and studied for the first time. This matrix contains complete information of the MIS mapping. A necessary and sufficient condition for the controllability of SBCN is obtained. The corresponding control and switching law, which drive a point to a given reachable point are designed. A sufficient condition for the observability of an SBCN is given. Moreover, under the assumption of controllability, one necessary and sufficient condition is derived for the observability.