摘要
In this paper,the problem of controllability of Boolean control networks(BCNs)with multiple time delays in both states and controls is investigated.First,the controllability problem of BCNs with multiple time delays in controls is considered.For this controllability problem,a controllability matrix is constructed by defining a new product of matrices,based on which a necessary and sufficient controllability condition is obtained.Then,the controllability of BCNs with multiple time delays in states is studied by giving a necessary and sufficient condition.Subsequently,based on these results,a controllability matrix for BCNs with multiple time delays in both states and controls is proposed that provides a concise controllability condition.Finally,two examples are given to illustrate the main results.
基金
supported by the Natural Science Foundation of Chongqing,China(No.CSTB2022NSCQ-MSX2869)
the Science and Technology Research Program of Chongqing Municipal Education Commission,China(No.KJQN202200524)
the Research Project of National Center for Applied Mathematics in Chongqing,China(No.ncamc2022-msxm05)
the Program of Chongqing Normal University,China(No.21XLB045)。
