Lyapunov Functions for the Set Stability and the Synchronization of Boolean Control Networks

We propose Lyapunov functions for the set stability of Boolean networks (BNs) and control Lyapunov functions for the feedback set stabilization and the synchronization of Boolean control networks (BCNs) in this brief. Meanwhile, some propositions of these Lyapunov functions are put forward. Sufficient and necessary conditions for the set stability of BNs, the feedback set stabilization of BCNs and the synchronization of drive-response coupled BCNs in the form of Lyapunov functions are presented successively. Moreover, an algorithm is given to construct control Lyapunov functions and state feedback controllers simultaneously for the synchronization of coupled BCNs. Two examples are given to illustrate the obtained results.