Set reachability of Markovian jump Boolean networks and its applications

This study investigates the set reachability of Markovian jump Boolean networks (MJBNs). Firstly, through comprehensive analysis, two kinds of set reachability, strong set reachability and weak set reachability, are defined. By using semi-tensor product of matrices, the considered MJBN is converted into a Markov chain which can not only describe the state transition of the MJBN synchronously, but also maintain its transition probability. Based on this, the set reachability problem of the MJBN is transformed into the reachability and convergence problems of the corresponding Markov chain. Then some necessary and sufficient conditions for set reachability of MJBNs are obtained. Finally, the observability and output stability problems of MJBNs are discussed as two applications of set reachability.