Further Results on Full-Actuation of Linear Boolean Control Networks

This paper investigates fully actuated linear Boolean networks. Firstly, by utilizing the Reed-Muller form, the relationship between the truth vector of the Boolean function and the indicator vector is revealed. Besides, the necessary and sufficient condition is provided to determine whether a Boolean control network is linear. Furthermore, a method to calculate the corresponding coefficient matrices is established. Then, the rank condition for fully actuated Boolean networks is presented, and the controller design method is given with the aid of logical submatrix. Finally, the effectiveness of the obtained results is demonstrated through an illustrative example.