Stochastic stability of Boolean networks with Markov jump

In this paper, we address the stochastic stability problem of Boolean networks with Markov jumping. Firstly, an algebraic expression of Markov switching Boolean networks is obtained by using the semi-tensor product. Based on such algebraic expression, a necessary and sufficient condition of stochastic stability is given. The control signal is then designed for Markov jumping Boolean control networks. Finally, the study of illustrative example shows that the new result obtained in this paper is effective in stochastic stability and control signal designing for the investigated Boolean network.