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This dissertation deals with the design of decentralized estimators for large scale interconnected systems. The systems are composed of several subsystems interconnected together. At each subsystem level a filter is designed to estimate local and/or interface variables. Kalman filtering and H{dollar}\\infty{dollar} filtering tools are used to derive decentralized estimators based on two different approaches namely, direct and indirect methods. A power system application is used to illustrate the proposed algorithms. In each method the decentralized filter design requires a subsystem model (local model) and a set of measurements. In the direct method additional measurements are needed for decentralization. In the indirect method local models that are completely decoupled from the rest of the system are derived and no extra measurements are required. Specifically: (1) The local model is obtained using a Hessenberg type transformation in the direct method. In the indirect method this model is obtained using a model reduction technique called the optimal aggregation method. (2) Based on the model obtained in the first step and a specified set of measurements Kalman filters and H{dollar}\\infty{dollar} filters are designed. Power systems are typical large scale interconnected systems suitable for decentralized implementations. The Load Frequency Control (LFC) Problem which deals with load-generation matching fits in this category and is used to illustrate the proposed schemes using a three area power system.