Convergence and State Reconstruction of Time-varying Multi-agent Systems from Complete Observability Theory

TL;DR

This paper applies complete observability theory to analyze convergence and state reconstruction in continuous-time multi-agent systems with switching interaction graphs, providing simple conditions for consensus and initial state recovery.

Contribution

It introduces an observability-based framework for consensus analysis and state reconstruction in multi-agent systems, including cases with negative weights.

Findings

Necessary and sufficient conditions for exponential consensus

Initial states can be reconstructed from edge signals

Method applies to systems with negative edge weights

Abstract

We study continuous-time consensus dynamics for multi-agent systems with undirected switching interaction graphs. We establish a necessary and sufficient condition for exponential asymptotic consensus based on the classical theory of complete observability. The proof is remarkably simple compared to similar results in the literature and the conditions for consensus are mild. This observability-based method can also be applied to the case where negatively weighted edges are present. Additionally, as a by-product of the observability based arguments, we show that the nodes' initial value can be recovered from the signals on the edges up to a shift of the network average.