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Stability Analysis for a Consensus System of a Group of Autonomous Agents with Time Delays

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Time Delay Systems: Methods, Applications and New Trends

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 423))

Abstract

This study addresses the consensus problem for a group of autonomous agents with second order dynamics and time-delayed communications. The constraints on the communication topology can be relatively relaxed to two: it is time invariant, and absolutely connected. This represents a large class of dynamics, of which a small subset is presented here: where all the agents in the group communicate with each other, and that the time delay incurred is constant and equal for all the communication channels. An efficient control structure of PD type is proposed to achieve consensus in the position and velocity of the agents. The proposed control law introduces a particular construction in the characteristic equation of the system, which is first factorized to dramatically simplify the stability analysis in the delay space. Then using cluster treatment of characteristic roots (CTCR) procedure a complete stability picture is obtained, taking into account the variations in the control parameters and the communication delay. Case studies and simulations results are presented to illustrate the analytical derivations.

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Author information

Authors and Affiliations

  1. Mechanical Engineering Department, University of Connecticut, Storrs, CT, USA

    Rudy Cepeda-Gomez & Nejat Olgac

Authors
  1. Rudy Cepeda-Gomez
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  2. Nejat Olgac
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Corresponding author

Correspondence to Rudy Cepeda-Gomez .

Editor information

Editors and Affiliations

  1. Dept. Mechanical Engineering, Northeastern University, Huntingdon Ave. 360, Boston, 02115, Massachusetts, USA

    Rifat Sipahi

  2. Technicka Street 4, Prague, 166 07, Czech Republic

    Tomáš Vyhlídal

  3. , CNRSSupélec, L2S (UMR CNRS 8506), rue Joliot Curie 3, Gif-sur-Yvette, 91192, France

    Silviu-Iulian Niculescu

  4. , Department of Electrical and Information, University of L’Aquila, Via G. Gronchi 18, L’Aquila, 67100, Italy

    Pierdomenico Pepe

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© 2012 Springer-Verlag GmbH Berlin Heidelberg

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Cepeda-Gomez, R., Olgac, N. (2012). Stability Analysis for a Consensus System of a Group of Autonomous Agents with Time Delays. In: Sipahi, R., Vyhlídal, T., Niculescu, SI., Pepe, P. (eds) Time Delay Systems: Methods, Applications and New Trends. Lecture Notes in Control and Information Sciences, vol 423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25221-1_9

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  • DOI: https://doi.org/10.1007/978-3-642-25221-1_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25220-4

  • Online ISBN: 978-3-642-25221-1

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