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Necessary and sufficient condition for average consensus of networked multi-agent systems with heterogeneous time delays

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  • Kazunori Sakurama
  • Kazushi Nakano

Abstract

This paper deals with an average-consensus problem of networked multi-agent systems with heterogeneous time delays. First, a necessary and sufficient condition is derived for multi-agent systems to achieve average consensus. This condition is represented in the form of an algebraic condition by using the delay-transition and the delay-weighted Laplacians. Second, a performance criterion is introduced to evaluate multi-agent systems that do not achieve average consensus. The criterion is represented in terms of the norms with respect to the above Laplacians. These results imply that the introduced Laplacians play important roles in analysing multi-agent systems with heterogeneous time delays. The validity of the analysis results is demonstrated by simulations with six-agent systems.

Suggested Citation

  • Kazunori Sakurama & Kazushi Nakano, 2015. "Necessary and sufficient condition for average consensus of networked multi-agent systems with heterogeneous time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(5), pages 818-830, April.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:5:p:818-830
    DOI: 10.1080/00207721.2013.798442
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    References listed on IDEAS

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    1. Jiahu Qin & Huijun Gao & Wei Xing Zheng, 2011. "On average consensus in directed networks of agents with switching topology and time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(12), pages 1947-1956.
    2. Lin, Peng & Jia, Yingmin, 2008. "Average consensus in networks of multi-agents with both switching topology and coupling time-delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 303-313.
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