On Existence and Design of Distributed Observer for Systems with Directed Communication

This paper investigates the state estimation problem of a distributed network testing system composed of N sensors. For the Luenberger-type observer design, they have the same observability. We first prove the existence of a class of observers under the condition of collective observability and strongly connected. The sensors network reconstructs all states under collective observability. The unobservable part is reconstructed via exchanging information with its neighbors. A consensus term is added to the traditional Luenberger observer to estimate the unobservable portions. The gain matrix design problem of local observer is solved. The asymptotic state reconstruction of communication topology and measurement information structure is realized on each sensor. Finally, the proposed observer is validated by simulation experiments.