In this paper, we propose a design method of hierarchical decentralized observers for networked linear systems. In this method, based on suitable state-space expansion of the network systems, we, first, find a high-dimensional dynamical compensator that can achieve any desirable performance for decentralized state estimation. Next, fully taking advantage of model reduction techniques, we extract a subspace that is essentially relevant to the decentralized state estimation, from the high-dimensional state-space of the dynamical compensator. This procedure successfully yields a lower-dimensional compensator that guarantees not only the stability of the estimation error but also a desirable estimation performance with respect to the system behavior for external input signals. The effectiveness of the proposed method is shown through an application to the state estimation of power networks.
