Skip to main content
SpringerLink
Log in

Robust synchronization of uncertain complex systems with time-varying delays

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

Synchronization analysis and design problems for uncertain time-delayed high-order complex systems with dynamic output feedback synchronization protocols are investigated. By stating projection on the synchronization subspace and the complement synchronization subspace, synchronization problems are transformed into simultaneous stabilization problems of multiple subsystems related to eigenvalues of the Laplacian matrix of the interaction topology of a complex system. In terms of linear matrix inequalities (LMIs), sufficient conditions for robust synchronization are presented, which include only five LMI constraints. By the changing variable method, sufficient conditions for robust synchronization in terms of LMIs and matrix equalities are given, which can be checked by the cone complementarily linearization approach. The effectiveness of theoretical results is shown by numerical examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. CAI N, ZHONG Y. Formation controllability of high-order linear time-invariant swarm systems [J]. IET Control Theory Appl, 2010, 4(4): 646–654.

    Article  MathSciNet  Google Scholar 

  2. XIAO F, WANG F, CHEN J, GAO Y. Finite-time formation control for multi-agent systems [J]. Automatica, 2009, 45(11): 2605–2611.

    Article  MATH  MathSciNet  Google Scholar 

  3. OLFATI-AABER R. Flocking for multi-agent dynamic systems: Algorithms and theory [J]. IEEE Trans Automat Control, 2006, 51(3): 401–420.

    Article  MathSciNet  Google Scholar 

  4. ABDESSAMEUD A, TAYEBI A. Attitude synchronization of a group of spacecraft without velocity measurements [J]. IEEE Trans. Automat Control, 2009, 54(11): 2642–2648.

    Article  MathSciNet  Google Scholar 

  5. FAX J A, MURRAY R M. Information flow and cooperative control of vehicle formations [J]. IEEE Trans Automat Control, 2004, 49(9): 1465–1476.

    Article  MathSciNet  Google Scholar 

  6. CHANG Lei-lei, LI Meng-jun, JIANG Jiang. A variable weight approach for evidential reasoning [J]. Journal of Central South University, 2013, 20(8): 2202–2211.

    Article  Google Scholar 

  7. JADBABAIE A, LIN J, MORSE A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules [J]. IEEE Trans Automat Control, 2003, 48(6): 988–1001.

    Article  MathSciNet  Google Scholar 

  8. OLFATI-SABER R, MURRAY R M. Consensus problems in networks of agents with switching topology and time-delays [J]. IEEE Trans Automat Control, 2004, 49(9): 1520–1533.

    Article  MathSciNet  Google Scholar 

  9. REN W. Consensus seeking, formation keeping, and trajectory tracking in multiple vehicle cooperative control [D]. Brigham: Brigham Young University, 2004.

    Google Scholar 

  10. BLIMAN P A, FERRARI-TRECATE G. Average consensus problems in networks of agents with delayed communications [J]. Automatica, 2008, 44(8): 1985–1995.

    Article  MATH  MathSciNet  Google Scholar 

  11. TIAN Y P, LIU C L. Consensus of multi-agent systems with diverse input and communication delays [J]. IEEE Trans Automat Control, 2008, 53(9): 2122–2128.

    Article  MathSciNet  Google Scholar 

  12. SEURET A, DIMAROGONAS D V, JOHANSSON K H. Consensus under communication delays [C]// IEEE Conf Decision and Control. 2008: 4922–4927.

    Google Scholar 

  13. SUN Y G, WANG L, XIE G. Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays [J]. Syst. Control Lett, 2008, 57(2): 175–183.

    Article  MATH  MathSciNet  Google Scholar 

  14. CHOPRA N, SPONG M W, LOZANO R. Synchronization of bilateral teleoperators with time delay [J]. Automatica, 2008, 44(8): 2142–2148.

    Article  MATH  MathSciNet  Google Scholar 

  15. LESTAS I, VINNICOMBE G. The S-hull approach to consensus [C]// IEEE Conf. Decision and Control, 2007: 182–187.

    Google Scholar 

  16. XIAO F, WANG L. Consensus problems for high-dimensional multi-agent systems [J]. IET Control Theory Appl, 2007, 1(3): 830–837.

    Article  Google Scholar 

  17. SHI Miao, LI Jun-min, HE Chao. Synchronization of complex dynamical networks with nonidentical nodes and derivative coupling via distributed adaptive control [J]. Mathematical Problems in Engineering, 2013: 172608.

    Google Scholar 

  18. CAI N, XI J, ZHONG Y. Necessary and sufficient conditions for asymptotic swarm stability of high order swarm systems [C]// IEEE Int Conf Control and Automation, IEEE. 2010: 1870–1875.

    Google Scholar 

  19. CAI N, XI J, ZHONG Y. Swarm stability of high-order linear time-invariant swarm systems [J]. IET Control Theory Appl, 2011, 5(2): 402–408.

    Article  MathSciNet  Google Scholar 

  20. XI J, CAI N, ZHONG Y. Consensus problems for high-order linear time-invariant swarm systems [J]. Physica A, 2010, 389(24): 5619–5627.

    Article  Google Scholar 

  21. PAN Huan, NIAN Xiao-hong, GUO Ling. Extended consensus analysis of multi-agent systems with switching topologies [J]. Journal of Central South University, 2012, 19(6): 1564–1569.

    Article  Google Scholar 

  22. NIAN Xiao-hong, SU Sai-jun, PAN Huan. Consensus tracking protocol and formation control of multi-agent systems with switching topology [J]. Journal of Central South University, 2011, 18(4): 1178–1183.

    Article  Google Scholar 

  23. MÜNZ U, PAPACHRISTODOULOU A, ALLGÖWER F. Generalized Nyquist consensus condition for high-order linear multi-agent systems with communication delays [C]// IEEE Conf Decision and Control. 2009: 4765–4771.

    Google Scholar 

  24. XI J, SHI Z, ZHONG Y. Consensus analysis and design for high-order linear swarm systems with time-varying delays [J]. Physica A, 2011, 390(23): 4114–4123.

    Article  Google Scholar 

  25. LI Z, DUAN Z, CHEN G, HUANG L. Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint [J]. IEEE Trans Circuits Syst I: Regular Papers, 2010, 57(1): 213–224.

    Article  MathSciNet  Google Scholar 

  26. SEO J H, SHIM H, BACK J. Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach [J]. Automatica, 2009, 45(11): 2659–2664.

    Article  MATH  MathSciNet  Google Scholar 

  27. LIU Y, JIA Y, DU J, YUAN S. Dynamic output feedback control for consensus of multi-agent systems: An H∞ approach [C]// Amer Control Conf., St. Louis, MO: IEEE 2009: 4470–4475.

    Google Scholar 

  28. XI J, SHI Z, ZHONG Y. Consensus and consensualization of high-order swarm systems with time delays and external disturbances [J]. J Dyn Syst Meas Control, 2012, 134(4): 1–7.

    Article  MathSciNet  Google Scholar 

  29. GODSIL CAND G R. Algebraic graph theory [M]. New York: Springer-Verlag, 2001.

    Book  Google Scholar 

  30. MOON Y S, PARK P, KWON W H, LEE Y S. Delay-dependent robust stabilization of uncertain state-delayed systems [J]. Int J Control, 2001, 74(4): 1447–1455.

    Article  MATH  MathSciNet  Google Scholar 

  31. PETERSEN I R. A stabilization algorithm for a class of uncertain linear systems [J]. Syst Control Lett, 1987, 8(4): 351–357.

    Article  MATH  Google Scholar 

  32. BOYD S, GHAOUI L E, FERON E, BALAKRISHNAN V. Linear matrix inequalities in system and control theory [M]. Philadelphia, PA: SIAM, 1994.

    Book  Google Scholar 

  33. GHAOUI L EL, USTRY F, AITRAMI M. A cone complementarity linearization algorithm for static output-feedback and related problems [J]. IEEE Trans Automat Control, 1997, 42(8): 1171–1176.

    Article  MATH  MathSciNet  Google Scholar 

  34. LIN P, JIA Y, LI L. Distributed robust H∞ consensus control in directed networks of agents with time-delay [J]. Syst Control Lett, 2008, 57(8): 643–653.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Xi’an Research Institute of High-tech, Xi’an, 710025, China

    Hai-long Li  (李海龙), Jian-xiang Xi  (席建祥), Hui Li  (李卉) & Yao-qing Cao  (曹耀钦)

Authors
  1. Hai-long Li  (李海龙)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian-xiang Xi  (席建祥)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hui Li  (李卉)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yao-qing Cao  (曹耀钦)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian-xiang Xi  (席建祥).

Additional information

Foundation item: Project(61374054) supported by the National Natural Science Foundation of China; Project(2013JQ8038) supported by the Shanxi Provincal Natural Science Foundation Research Projection, China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Hl., Xi, Jx., Li, H. et al. Robust synchronization of uncertain complex systems with time-varying delays. J. Cent. South Univ. 22, 584–592 (2015). https://doi.org/10.1007/s11771-015-2559-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-015-2559-x

Key words

Search

Navigation