Distributed State Estimation of Discrete-Time LTI Systems via Jordan Canonical Representation

TL;DR

This paper presents a novel distributed state estimation method for discrete-time LTI systems using Jordan canonical form, enabling nodes to estimate system states collaboratively with improved flexibility and less restrictive conditions.

Contribution

It introduces a Jordan canonical form-based distributed estimation scheme with necessary and sufficient conditions for convergence, enhancing previous methods by increasing design flexibility.

Findings

Ensures asymptotic convergence of local estimates to true state

Provides less restrictive conditions for distributed observer existence

Offers greater flexibility in coupling gain selection

Abstract

In this paper, we address the problem of distributed state estimation for a discrete-time, linear time-invariant system. Building on the framework proposed in [2], we exploit the Jordan canonical form of the system matrix to develop a distributed estimation scheme that ensures the asymptotic convergence of the local state estimates to the true system state. The proposed approach relies on the idea that each node reconstructs the components of the system state that are detectable for it through a local Luenberger observer, while employing a consensus-based strategy to estimate the undetectable components. Necessary and sufficient conditions for the existence of a distributed observer that guarantees asymptotic estimation accuracy are derived. Compared with the previous work [2], the proposed design offers greater flexibility in the selection of the coupling gains and leads to a less restrictive set of conditions for solvability.