Stabilizability analysis and switching signals design of switched Boolean networks

Stabilizability analysis and stabilizable switching signals design of switched Boolean networks (SBNs) are further investigated via semi-tensor product of matrices in this paper. First, two kinds of stabilizability of SBNs, stabilizability under arbitrary switching signals and pointwise stabilizability, are discussed under the framework of an improved approach. Second, more general stable structures, kernel attractors, are defined and studied. Subsequently, several necessary and sufficient conditions are derived to ascertain that an SBN is stabilizable under arbitrary switching signals or pointwise stabilizable to a kernel attractor. Then a constructive method is presented to determine all stabilizable switching signals dependent on states (SSDSs), which drive the considered network stabilizable to a fixed point, a kernel attractor or a set. Finally, two examples are given to show the effectiveness of the obtained results.