Controllability of Boolean control networks with multiple bounded time-varying delays

This work investigates controllability of Boolean control networks (BCNs) with multiple time-varying time-delays. Under the framework of the semi-tensor product (STP) of matrices, the standard algebraic form of BCNs with multiple time-varying time-delays is introduced based on which the controllability matrices are defined. An iteration algorithm is proposed to calculate the controllability matrices which leads to a criterion for controllability. Especially, a necessary and sufficient for the controllability of BCNs with multiple periodic time-delays is obtained. An illustrative example is provided to illustrate the main results obtained in this paper.