Stability analysis for switched singular Boolean networks

The stability analysis of gene regulatory networks is a hot topic in systems biology. We investigate the stability of switched singular Boolean networks (SSBNs) by using the semi-tensor product of matrices. First, the dynamics of SSBNs is converted to an algebraic form, based on which a necessary and sufficient condition is established for the uniqueness of solution of SSBNs. Second, several necessary and sufficient conditions are presented for the stability of SSBNs under arbitrary switching signal and the switching stabilizability of SSBNs, respectively, by converting an SSBN into an equivalent switched Boolean network. Two illustrative examples are presented to show that the main results obtained in this paper are effective in analyzing the stability of SSBNs.