Controllability of Boolean Control Networks with Time-delay

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  This paper investigates the controllability of Boolean control networks(BCN)with time-delays in state by using the semi-tensor product of matrices.The definition of controllability matrices for BCNs with time-delays is introduced and an iterative algorithm is proposed to calculate all of the k-step controllability matrices and the controllability matrix for any given BCN with time-delay.And by using the controllability matrices,a necessary and sufficient condition for the controllability of BCNs is given.An algorithm is proposed to obtain the control sequences that steer the system from the initial state to any given reachable destination state.An illustrative example is also provided to illustrate the main results obtained in this paper.
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