Pinning Control Design for Stabilizing Large-Scale Markovian Jump Boolean Networks

This article develops pinning control strategies to achieve global asymptotic stabilization in large-scale Markovian jump Boolean networks (MJBNs), closely linking their stability to network structural characteristics. First, the considered MJBN is divided into several sub-MJBNs, where signals switch according to irreducible transition probability matrices. Second, the stability of these sub-MJBNs is mapped onto that of deterministic periodic BNs. This transformation facilitates the formulation of a network-structure-based stability criterion for MJBNs by converting the inherently random stability characteristics of the networks into those of deterministic networks. Third, applying this criterion, static pinning control (SPC) is devised to stabilize MJBNs, where effective pinning nodes are identified by finding a feedback vertex set in the corresponding n-vertex digraph. Consequently, this method addresses the challenges associated with large-scale MJBNs effectively. To demonstrate the practical applicability of our theoretical findings, two biological examples are presented.