Distributed exponential state estimation of linear systems over jointly connected switching networks

TL;DR

This paper enhances distributed state estimation for linear systems over switching networks by proving exponential convergence and allowing distinct coupling gains, improving robustness and design flexibility.

Contribution

It extends previous work by strengthening convergence from asymptotic to exponential and enabling different coupling gains in local observers.

Findings

Establishes exponential stability for certain linear time-varying systems.

Demonstrates guaranteed convergence rate and robustness to disturbances.

Provides greater flexibility in observer design.

Abstract

Recently, the distributed state estimation problem for continuous-time linear systems over jointly connected switching networks was solved. It was shown that the estimation errors will asymptotically converge to the origin by using the generalized Barbalat's Lemma. This paper further studies the same problem with two new features. First, the asymptotic convergence is strengthened to the exponential convergence. This strengthened result not only offers a guaranteed convergence rate, but also renders the error system total stability and thus is able to withstand small disturbances. Second, the coupling gains of our local observers can be distinct and thus offers greater design flexibility, while the coupling gains in the existing result were required to be identical. These two new features are achieved by establishing exponential stability for two classes of linear time-varying systems, which may have other applications.