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Organically-structured control problem based on state observer for a class of large-scale systems with expanding construction is studied in this paper. The problem is how to design the local state feedback controller and observer of the new subsystem added into original large scale system, but not changing the decentralized state feedback control laws of original construction, so that both the new subsystem and the resultant expanded system are robust decentralized connective stable. First, the mathematical model of the large-scale system with expanded construction, which possesses the state observers, is analyzed. Then, the sufficient condition of the robust decentralized connective stabilization for the expanded construction of large-scale systems is deduced by taking Lyapunov theory and LMI approach, and the problem is transformed into how to solve a linear matrix inequality (LMI). The design method of the organically-structured controller and observer of the expanded construction is given. At last, a simulation example shows the effectiveness of presented method.