The containment problem of finite-field networks (FFNs) with fixed topology (FT-FFNs) and switching topology (ST-FFNs) is studied. Firstly, the concept of containment for FFNs is proposed. Secondly, by semi-tensor product (STP) of matrices, the logical updating rule of FFNs with multiple leaders can be equivalently converted into an algebraic form. Thirdly, the containment problem is converted into the problem of set stability, and an easily verifiable necessary and sufficient condition is presented to achieve containment. In addition, the obtained results are applied to the containment problem of ST-FFNs. Finally, two examples support the effectiveness of the main results.

研究了具有固定拓扑结构 (FT-FFNs) 和交换拓扑结构 (ST-FFNs) 的有限域网络 (FFNs) 的包含问题。首先，提出了FFNs的遏制概念。其次，通过矩阵的半张量积（STP），可以将具有多个领导者的 FFN 的逻辑更新规则等价转换为代数形式。第三，将包容问题转化为集合稳定性问题，提出了一个容易验证的充要条件来实现包容。此外，所得结果还应用于 ST-FFN 的包含问题。最后，两个例子支持了主要结果的有效性。