Further results on feedback stabilization control design of Boolean control networks

This paper investigates designing all possible feedback stabilizers for Boolean control networks (BCNs). Some new results on the feedback stabilization control design of BCNs are presented. The main tool used in the paper is the semi-tensor product of matrices. First, the complete family of reachable sets is defined for BCNs. Then it is shown that all the complete families of reachable sets determine all possible state feedback stabilizers. Second, using all the complete families of reachable sets, all possible state feedback stabilizers are obtained. Third, a necessary and sufficient condition is obtained for the existence of output feedback stabilizers. Based on this condition, all possible output feedback stabilizers are designed for BCNs. Finally, the obtained new results are applied to the regulation of the lactose operon in Escherichia coli.