Simultaneous stabilization of Boolean control networks via semi-tensor product method

The simultaneous stabilization of a collection of Boolean control networks (BCN) is investigated in this paper, and several controllers are designed. The dynamics of each BCN is converted to a discrete-time bilinear system by using the semi-tensor product of matrices and matrix expression of logical functions, based on which the simultaneous stabilization of the collection of BCNs is then studied. Main results contain two parts: (i) two sufficient conditions and two necessary and sufficient conditions are obtained for the simultaneous stabilization of a group of neat BCNs by feedback control, including state feedback and output feedback, and (ii) for non-neat BCNs, by introducing some auxiliary state and output variables, the group of BCNs are converted into the neat ones, and then several sufficient conditions and necessary and sufficient conditions are established for the simultaneous stabilization.