布尔控制网络的输出稳定与镇定
Output stability and stabilization of Boolean control networks

矩阵的半张量积是将逻辑变量转化为向量研究的主要工具. 本文利用半张量积把逻辑控制系统表示为离散时 间仿射线性系统, 在逻辑系统的状态空间框架下研究了以布尔控制网络为代表的逻辑动态系统的输出稳定与镇定. 首先 给出布尔网络输出稳定的定义, 研究了布尔网络输出稳定的充要条件; 其次讨论了布尔控制网络的输出镇定, 分别得到 了布尔控制网络由常值输入变量、自由控制序列、状态反馈控制序列输出镇定的条件. 本文讨论的系统输出稳定与镇定 是(部分)变量稳定与镇定的推广.
Semi-tensor product of matrices is the main tool in converting logical variable to its vector form. Using semi-tensor product of matrices, the logical dynamical system is converted to discrete time affine linear system. Under framework of state space expression of Boolean network, the output stability and output stabilization are discussed in this paper. First, the definition of output stability of Boolean network is given, and the necessary and sufficient condition for output stability of Boolean network is obtained. Second, the output stabilization of Boolean control network is investigated and the different conditions for output stabilization are obtained. The output stability and stabilization discussed in this paper are generalizations of the known state stability and stabilization.