Consider that an autonomous linear time-invariant (LTI) plant is given andthat a network of LTI observers assesses its output vector. The disseminationof information within the network is dictated by a pre-specified directed graphin which each vertex represents an observer. Each observer computes its ownstate estimate using only the portion of the output vector accessible to it andthe state estimates of other observers that are transmitted to it by itsneighbors, according to the graph. This paper proposes an update rule that is anatural generalization of consensus, and for which we determine necessary andsufficient conditions for the existence of parameters for the update rule thatlead to asymptotic omniscience of the state of the plant at all observers. Theconditions reduce to certain detectability requirements that imply that ifomniscience is not possible under the proposed scheme then it is not viableunder any other scheme that is subject to the same communication graph,including nonlinear and time-varying ones.
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