Set stabilizability of switched Boolean control networks via Ledley antecedence solution

Abstract

This paper studies two kinds of set stabilizability issues of switched Boolean control networks (SBCNs) by Ledley antecedence solution, that is, pointwise set stabilizability and set stabilizability under arbitrary switching signals. Firstly, based on the state transition matrix of SBCNs, the mode-dependent truth matrix is defined. Secondly, using the mode-dependent truth matrix in every step, a switching signal and the corresponding Ledley antecedence solutions are determined. Furthermore, a state feedback switching signal and a state feedback control are obtained for the pointwise set stabilizability. Thirdly, with the help of all mode-dependent truth matrices, the Ledley antecedence solutions are derived for a set of Boolean inclusions, which admits a state feedback control for the set stabilizability under arbitrary switching signals. Finally, an example is given to show the effectiveness of the proposed results.