Set Stability and Stabilization of Switched Boolean Networks With State-Based Switching

Abstract

This paper is devoted to studying the set stability and stabilization of switched Boolean networks (SBNs) with state-based switching using the semi-tensor product (STP) of matrices. First, the algebraic form of an SBN is obtained by STP. Then, a necessary and sufficient condition for set stability is presented for a given set and state-based switching matrix. In addition, state-based switching matrices are designed such that systems can be stabilized to a given set. The selection strategy for pinning nodes is also given, and pinning controllers are designed such that systems can achieve set stabilization via a state-based switching matrix. Finally, examples are provided to illustrate the effectiveness of the obtained results.