Set stability for switched Boolean networks with open-loop and closed-loop switching signals

Abstract

This paper mainly analyzes the set stability of switched Boolean networks (SBNs) by considering two different methods of switching signals in the form of open-loop and closed-loop switching. First, the definitions of set stability are proposed for SBNs with such switching signals. Then, we propose two different algorithms to find the largest open-loop switching invariant set and largest closed-loop switching invariant set. Furthermore, the corresponding set stability conditions for SBNs are given in each case. In addition, the constructive procedures are presented to design the switching signal sequence to achieve set stability under the two different methods of switching signals. Finally, the effectiveness of the proposed algorithms and research results are demonstrated using two numerical examples.