Multi‐angle analysis of stabilization of linear finite field networks

Abstract This study presents a comparative analysis of three representative methods—the state‐space method, the high‐order fully actuated system (HOFAS) approach, and the semi‐tensor product (STP) method—for addressing the stabilization problem of finite field networks (FFNs). Unlike traditional linear systems over real‐number fields, FFNs operate within discrete algebraic structures. The presence of non‐split matrices and the absence of eigen‐decomposition render conventional controllability criteria and stabilization strategies inapplicable. To address these challenges, the three methods are systematically formulated and analyzed within a unified framework. Their theoretical characteristics are investigated in terms of controllability conditions and feedback design feasibility. Comparative simulations, including both split and non‐split network examples over , demonstrate the respective strengths and limitations of each method. The results indicate that the state‐space method offers intuitive interpretability, the HOFAS approach provides greater flexibility in handling high‐dimensional and non‐split systems, and the STP method exhibits universal applicability to arbitrary FFN. Overall, this comparative analysis clarifies the applicability boundaries of existing algebraic control techniques and provides theoretical guidance for selecting design strategies for FFNs.