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Consensus Problems in Networks of Agents With Switching Topology and Time-Delays

2004/09/01 by R. Olfati-Saber, Reza Olfati‐Saber, Richard M. Murray +1 · 12,780 citations
Computer Science · Mathematics · #Algebraic connectivity #Algebraic graph theory #Algorithm #Artificial intelligence #Computer science #Consensus #Convergence (economics) #Directed graph #Distributed Control Multi-Agent Systems #Function (biology) #Graph #Graph theory #Laplacian matrix #Lyapunov function #Mathematics #Multi-agent system #Network topology #Neural Networks Stability and Synchronization #Opportunistic and Delay-Tolerant Networks #Theoretical computer science #Topology (electrical circuits) #Uniform consensus

paper · doi:10.1109/tac.2004.834113

published in IEEE Transactions on Automatic Control 49(9), 1520-1533 (Institute of Electrical and Electronics Engineers)

openalex publication_date 2004/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.

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