A simply structured distributed observer is described for estimating the state of a discrete-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to construct the local estimators which comprise the observer so that their state estimation errors all converge exponentially fast to zero at a fixed, but arbitrarily chosen rate provided the network's graph is strongly connected for all time. This is accomplished by exploiting several well-known properties of invariant subspaces plus several kinds of suitably defined matrix norms.
@article{arxiv.1903.05486,
title = {A Distributed Observer for a Discrete-Time Linear System},
author = {Lili Wang and Ji Liu and A. Stephen Morse and Brian D. O. Anderson},
journal= {arXiv preprint arXiv:1903.05486},
year = {2019}
}