On Full-Actuation of Linear Boolean Control Networks

This paper investigates fully actuated linear Boolean networks. Firstly, using semi-tensor product of matrices, necessary and sufficient conditions are provided to determine whether a Boolean (control) network is linear. Furthermore, a suitable algorithm is established to calculate corresponding coefficient matrices if the considered Boolean control network is linear. Then, the definition of the fully actuated discrete linear systems is generalized to that of Boolean networks for the first time. On the basis of equivalent condition obtained to determine the full-actuation of Boolean control networks, it is revealed that two definitions of full actuation, which are respectively for linear systems and Boolean networks, are consistent. Finally, effectiveness of obtained results is shown by an illustrative example.