A Distributed Observer for a Continuous-Time Linear System with time-varying network

TL;DR

This paper introduces a distributed observer for continuous-time linear systems with time-varying network topology, ensuring exponential convergence of state estimates under various switching conditions.

Contribution

It presents a simple structured observer design with conditions for gain selection that guarantees exponential convergence despite network switching.

Findings

Observer guarantees exponential convergence with fixed rate.

Conditions for gain design under switching network graphs.

Existence of gain when network's stochastic matrix is doubly stochastic.

Abstract

A simply structured distributed observer is described for estimating the state of a continuous-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to design a gain $g$ in 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. A linear inequality for $g$ is provided when the network's graph is switching according to a switching signal with a dwell time or an average dwell time, respectively. It has also been shown the existence of $g$ when the stochastic matrix of the network's graph is chosen to be doubly stochastic under arbitrarily switching signals. This is accomplished by exploiting several well-known properties of invariant subspaces and properties of perturbed systems.