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Consensus Problem of Delayed Linear Multi-agent Systems pp 13–43Cite as

Consensus of Homogeneous Multi-agent Systems with Time Delays

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Abstract

With the help of various analysis methods, including frequency-domain analysis, Lyapunov method, properties of stochastic matrix theory, etc., delay effect on consensus seeking multi-agent systems, especially for the homogeneous multi-agent systems , has been extensively analyzed in the past decade. With nonnegligible communication delay , however, consensus results are mainly for the first-order, second-order, and high-order multi-agent systems driven by stationary consensus algorithms with diverse communication delays, dynamical consensus algorithm in synchronously coupled form, etc. Besides, consensus problem with identical input delay has also been extensively studied, but consensus analysis of multi-agent systems with diverse input delays only attracted a little attention.

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References

  1. R. Olfati-Saber, R. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)

    Article  MathSciNet  Google Scholar 

  2. Y.P. Tian, C.L. Liu, Consensus of multi-agent systems with diverse input and communication delays. IEEE Trans. Autom. Control 53(9), 2122–2128 (2008)

    Article  MathSciNet  Google Scholar 

  3. R. Pedrami, B.W. Gordon, Control and analysis of energetic swarm systems, in 2007 American Control Conference (New York, USA, 2007), pp. 1894–1899

    Google Scholar 

  4. C.A. Desoer, Y.T. Wang, On the generalized Nyquist stability criterion. IEEE Trans. Autom. Control 25(2), 187–196 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  5. I. Lestas, G. Vinnicombe, Scalable robustness for consensus protocols with heterogeneous dynamics, in 16th IFAC World Congress (Prague, Czech Republic, 2005)

    Google Scholar 

  6. Y.P. Tian, G. Chen, Stability of the primal-dual algorithm for congestion control. Int. J. Control 79(6), 662–676 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. D.J. Lee, M.K. Spong, Agreement with non-uniform information delays, in 2006 American Control Conference (Minneapolis, MN, USA, 2006), pp. 756–761

    Google Scholar 

  8. Y.P. Tian, C.L. Liu, Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations. Automatica 45(5), 1347–1353 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. W. Yang, A.L. Bertozzi, X.F. Wang, Stability of a second order consensus algorithm with time delay, in 47th IEEE Conference on Decision and Control (Cancun, Mexico, 2008), pp. 2926–2931

    Google Scholar 

  10. R. Cepeda-Gomez, N. Olgac, An exact method for the stability analysis of linear consensus protocols with time delay. IEEE Trans. Autom. Control 56(7), 1734–1740 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Z. Meng, W. Ren, Y. Cao, Z. You, Leaderless and leader-following consensus with communication and input delays under a directed network topology. IEEE Trans. Syst. Man Cybern. B Cybern. 41(1), 75–88 (2011)

    Article  Google Scholar 

  12. P. Lin, Y. Jia, J. Du, S. Yuan, Distributed consensus control for second-order agents with fixed topology and time-delay, in 26th Chinese Control Conference (Zhangjiajie, China, 2007), pp. 577–581

    Google Scholar 

  13. U. Munz, A. Papachristodoulou, F. Allgoewer, Delay robustness in consensus problems. Automatica 46(8), 1252–1265 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. W. Yu, G. Chen, M. Cao, Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica 46(6), 1089–1095 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. C.L. Liu, F. Liu, Asynchronously-coupled consensus of second-order dynamic agents with communication delay. Int. J. Innov. Comput. Inf. Control 6(11), 5035–5046 (2010)

    Google Scholar 

  16. C.L. Liu, F. Liu, Consensus problem of second-order dynamic agents with heterogeneous input and communication delays. Int. J. Comput. Commun. Control 5(3), 325–335 (2010)

    Article  Google Scholar 

  17. C.L. Liu, F. Liu, Consensus problem of coupled autonomous agents with time delays. Acta Phys. Sin. 60(3), 030302 (2011)

    Google Scholar 

  18. C.L. Liu, F. Liu, Consensus analysis for multiple autonomous agents with input delay and communication delay. Int. J. Control Autom. Syst. 10(5), 1005–1012 (2012)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Automation, Jiangnan University, Wuxi, Jiangsu, China

    Cheng-Lin Liu & Fei Liu

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  1. Cheng-Lin Liu
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  2. Fei Liu
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Correspondence to Cheng-Lin Liu .

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Liu, CL., Liu, F. (2017). Consensus of Homogeneous Multi-agent Systems with Time Delays. In: Consensus Problem of Delayed Linear Multi-agent Systems. SpringerBriefs in Electrical and Computer Engineering(). Springer, Singapore. https://doi.org/10.1007/978-981-10-2492-4_2

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  • DOI: https://doi.org/10.1007/978-981-10-2492-4_2

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2491-7

  • Online ISBN: 978-981-10-2492-4

  • eBook Packages: EngineeringEngineering (R0)

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