Stability and Pinning Stabilization of Markovian Jump Boolean Networks

Abstract

This brief investigates stability and pinning stabilization of Markovian jump Boolean networks (MJBNs) based on semi-tensor product of matrices. New stability conditions for MJBNs are obtained directly by the algebraic expression of MJBNs, which lays a foundation for pinning control of MJBNs. Then, two algorithms are devised, one of which can get a stochastically stable MJBN easily and the other one generates a set of pinning nodes with the smallest cardinality. Moreover, all the feasible pinning controllers can be designed by solving a group of matrix equations. Illustrative examples are presented to show the effectiveness of the obtained results.