A Distributed Observer for a Discrete-Time Linear System

TL;DR

This paper introduces a distributed observer for discrete-time linear systems with outputs spread over a dynamic network, ensuring exponential convergence of state estimates under strong connectivity.

Contribution

It presents a novel method to design local estimators that guarantee exponential convergence in time-varying networks, leveraging invariant subspaces and matrix norms.

Findings

Estimates converge exponentially fast to true states.

The method works for strongly connected, time-varying networks.

Local estimators are constructed using invariant subspace properties.

Abstract

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.