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Consensus of Networked Multi-agent Systems with Delays and Fractional-Order Dynamics

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Consensus and Synchronization in Complex Networks

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

This chapter is devoted to studying the consensus problem of networked multi-agent systems with delays and fractional-order dynamics. The effects of input delay, communication delay, fractional-order dynamics and directed information flow on the consensus behavior of networked multi-agent systems are systematically studied. We find that consensus is very robust against communication delays in both integer-order systems and fractional-order systems with fractional-order α ∈ (0, 1]. One well-informed leader is proved to be enough for the regulation of all agents’ final state, even when the external signal is very weak. By using the generalized Nyquist stability criterion, a necessary and sufficient condition is derived to ensure the consensus of fractional-order systems with identical input delays over directed networks. Furthermore, when the interaction topology is undirected, consensus condition of fractional-order systems with heterogeneous input delays is explicitly given. Based on frequency-domain approach, sufficient conditions are obtained to ensure the consensus of the fractional-order systems with simultaneously nonuniform input and communication delays.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Jianquan Lu & Jinde Cao

  2. Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415, Potsdam, Germany

    Jianquan Lu & Jürgen Kurths

  3. Department of Mechanical Engineering, University of Hong Kong, Hong Kong, China

    Jun Shen

Authors
  1. Jianquan Lu
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  2. Jun Shen
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  3. Jinde Cao
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  4. Jürgen Kurths
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Correspondence to Jianquan Lu .

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Editors and Affiliations

  1. Macedonian Academy of Sciences and Arts, Bul.Krste Misirkov 2, Skopje, 1000, Macedonia

    Ljupco Kocarev

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Lu, J., Shen, J., Cao, J., Kurths, J. (2013). Consensus of Networked Multi-agent Systems with Delays and Fractional-Order Dynamics. In: Kocarev, L. (eds) Consensus and Synchronization in Complex Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33359-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-33359-0_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33358-3

  • Online ISBN: 978-3-642-33359-0

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