Mean square stability for Markov jump Boolean networks

In this paper, one of the stability definitions of Markov jump Boolean networks (MJBNs), called mean square stability (MSS), is investigated. Some necessary and sufficient conditions are presented to guarantee the MSS of such MJBNs. Moreover, one of the necessary and sufficient conditions for MSS is obtained in terms of linear programming, which implies that MSS is equivalent to global stability with probability 1 for MJBNs. Furthermore, the construction of Lyapunov function is given and also another theorem based on the Lyapunov function is derived to ensure the MSS of MJBNs. Finally, a numerical example is provided to illustrate the profits of our results.