In genetic regulatory networks, a stable configuration can represent the evolutionary behavior of cell death or unregulated growth in genes. We present analytical investigations on output feedback stabilizer design of Boolean networks (BNs) to achieve global stabilization via the semi-tensor product method. Based on network structure information describing coupling connections among nodes, an output feedback stabilizer is designed to achieve global stabilization. Compared with the traditional pinning control design, the output feedback stabilizer design is not based on the state transition matrix of BNs, which can efficiently determine pinning control nodes and reduce computational complexity. Our proposed method is efficient in that the calculation of the state transition matrix with dimension 2ⁿ × 2ⁿ is avoided; here n is the number of nodes in a BN. Finally, a signal transduction network and a D. melanogaster segmentation polarity gene network are presented to show the efficiency of the proposed method. Results are shown to be simple and concise, compared with traditional pinning control for BNs.

在遗传调控网络中，稳定的构型可以代表细胞死亡或基因不受调控的生长的进化行为。我们目前对布尔网络（BN）的输出反馈稳定器设计进行分析研究，以通过半张量积方法实现全局稳定。基于描述节点之间耦合连接的网络结构信息，设计输出反馈稳定器以实现全局稳定。与传统的钉扎控制设计相比，输出反馈稳定器设计不基于BN的状态转移矩阵，可以有效地确定钉扎控制节点并降低计算复杂度。我们提出的方法之所以有效，是因为计算尺寸为2 ⁿ ×2的状态转移矩阵ⁿ被避免；这里n是BN中的节点数。最后，提出了一种信号转导网络和D. melanogaster分割极性基因网络，以证明该方法的有效性。与传统的BN钉扎控制相比，结果显示简单明了。