Necessary and sufficient conditions for the stabilizability of a class of LTI distributed observers

Consider that an autonomous LTI plant is given and that a network of local observers assesses the output vector of the plant. Each local observer in the network is LTI and measures a portion of the output vector. Each local observer computes a state estimate using its measurements and the state estimates of other local observers shared according to a preselected neighborhood structure. This paper proposes an update rule that is a natural generalization of consensus, and for which we determine necessary and sufficient conditions for the existence of parameters that lead to asymptotic omniscience of the state of the plant at all local observers.