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The problem of robust connective stabilities is considered in this paper for a class of large-scale uncertain interconnected power systems in the case of uncertain structural reconfigurations. Robust connective stability is defined based on the interconnected matrix and the load normalization factor uncertainties of power systems. A new analysis method with a robust degree is presented to establish a sufficient condition of connective stability for the system and the robustness bound for uncertainty parameters, by using the property of norms, eigenvalues and global parameters of the system matrices. The proposed method is applied to a two-area power system, and it shows the effectiveness of given conditions.