Abstract
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.
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