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Interdependent networks have become a hot research direction in the field of complex networks in recent years. At present, the research of interdependent networks mainly focuses on interdependent networks composed of two sub-networks, but complex systems in the real world may be composed of multiple subnetworks. This paper constructs a multi-dependent network model, studies its node failure mechanism and robustness issues, and conducts theoretical analysis of the robustness of three typical network combinations (non-ring structure, ring structure and mesh structure). The research results show that the robustness of the multi-layer interdependent network is related to the coupling strength between sub-networks, the average degree of external connections, the average degree of internal connections, and the number of sub-network nodes, and the performance of the characteristics is closely related to the network structure.