A simple approach to distributed observer design for linear systems

TL;DR

This paper presents a straightforward method for designing distributed observers for continuous-time LTI systems, ensuring error convergence under certain network connectivity conditions, with design reduced to solving LMIs.

Contribution

It offers a simple proof and design procedure for distributed observers using graph balancing and LMIs, improving understanding and implementation.

Findings

Distributed observers exist for observable systems with strongly connected graphs.

Estimation error can be made to decay at any pre-specified rate.

Design reduces to solving linear matrix inequalities.

Abstract

This note investigates the distributed estimation problem for continuous-time linear time-invariant (LTI) systems observed by a network of observers. Each observer in the network has access to only part of the output of the observed system, and communicates with its neighbors according to a given network graph. In this note we recover the known result that if the observed system is observable and the network graph is a strongly connected digraph, then a distributed observer exists. Moreover, the estimation error can be made to converge to zero at any a priori given decay rate. Our approach leads to a relatively straightforward proof of this result, using the mirror of the balanced graph associated with the original network graph. The numerical design of our distributed observer is reduced to solving linear matrix inequalities (LMI's). Each observer in the network has state dimension equal to that of the observed plant.