Controllability for a special case of multi-level Boolean control networks

This paper investigates controllability problem for multi-level Boolean control networks (BCNs). In this paper, the controllability is investigated and two notions of controllability are presented, i.e. group-controllability and simultaneous-controllability. By resorting to Perron-Frobenius theorem, necessary and sufficient criteria are obtained to guarantee group-controllability and simultaneous-controllability respectively. Finally, a numerical example is presented to show the validness of our main results.