Stability of Switched Boolean Networks with Restricted Successors

This study proposes a novel method for the set stability analysis of switched Boolean networks(SBNs) under restricted successors based on the semi-tensor product(STP) of matrices. We demonstrate that all allowable switching signals can be generated by a logic dynamical system (LDS) with free inputs, termed as the generator of switching signals(GSS). Thus, we regard the GSS as a part of the system through series interconnection and transfer the original restricted SBN into a logic system with free inputs. Then, we merge the GSS and the SBN using the STP and prove that the set stability of the original restricted SBN is equivalent to that of the merged LDS under arbitrary switching. Based on this, a necessary and sufficient condition of set stability is obtained. Further, a numerical example is provided to illustrate the use of the proposed result.