# Distributed State Estimation for Jointly Observable Linear Systems over Time-varying Networks

## TL;DR

This paper introduces a distributed observer approach for jointly observable linear systems over time-varying networks, ensuring exponential convergence under average connectivity conditions, applicable even with disconnected networks at each instant.

## Contribution

It provides sufficient conditions for distributed observers over periodic and switching networks, including cases with disconnected networks, using an averaging approach for exponential convergence.

## Key findings

- Distributed observer guarantees exponential convergence under average connectivity.
- Applicable to systems with eigenvalues with positive real parts.
- Validated through practical examples and applications.

## Abstract

This paper deals with a distributed state estimation problem for jointly observable multi-agent systems operated over various time-varying network topologies. The results apply when the system matrix of the system to be observed contains eigenvalues with positive real parts. They also can apply to situations where the communication networks are disconnected at every instant. We present sufficient conditions for the existence of distributed observers for general linear systems over periodic communication networks. Using an averaging approach, it is shown that the proposed distributed observer can provide exponentially converging state estimates of the state of the linear system when the network is uniformly connected on average. This average connectedness condition offers a more relaxed assumption that includes periodic switching, Markovian switching and Cox process switching as special cases. All the agents in the network share the estimated state with their neighbours through the network and cooperatively reconstruct the entire state locally. Furthermore, this study presents two exponential stability results for two classes of switched systems, providing valuable tools in related distributed state estimation approaches. A toy example and three practical applications are provided to illustrate the effectiveness of the theoretical results.

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Source: https://tomesphere.com/paper/2302.12161