Set Stability of Boolean Networks From Initial Set to Destination Set

This paper considers set stability of Boolean networks (BNs) from initial set to destination set. The existing set stability is the stability that for any initial state, i.e., there exists a finite time, such that the trajectory from any initial state belongs to the given subset after finite time. But in some cases, the interests may be not the whole state space, only a subset of the whole state space, such as the partial synchronization of a collection of locally interconnected systems. In this paper, we study the the set stability of BNs from initial set to destination set. The technique used in this paper is semi-tensor product of matrices. First, a necessary and sufficient condition is presented for set stability from initial set to destination set. Then as the application, stabilization of Boolean control network (BCN) via state-based networked controller is considered and a necessary and sufficient condition is provided. Finally, an example is provided to interpret the results.