About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 627060, 8 pages
http://dx.doi.org/10.1155/2014/627060
Research Article

Pinning Synchronization of One-Sided Lipschitz Complex Networks

1School of Information Engineering, Huanghuai University, Henan 463000, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
3Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 23 January 2014; Accepted 19 March 2014; Published 13 April 2014

Academic Editor: Zhiqiang Zuo

Copyright © 2014 Fang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. W. Wu, Synchronization in Complex Networks of Nonlinear Dynamical Systems, World Scientific, Singapore, 2007.
  2. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, “Synchronization in complex networks,” Physics Reports, vol. 469, no. 3, pp. 93–153, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  3. L. M. Pecora and T. L. Carroll, “Master stability functions for synchronized coupled systems,” Physical Review Letters, vol. 80, no. 10, pp. 2109–2112, 1998. View at Scopus
  4. C. W. Wu, “Synchronization in networks of nonlinear dynamical systems coupled via a directed graph,” Nonlinearity, vol. 18, no. 3, pp. 1057–1064, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. W. Lu and T. Chen, “New approach to synchronization analysis of linearly coupled ordinary differential systems,” Physica D. Nonlinear Phenomena, vol. 213, no. 2, pp. 214–230, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, “Synchronizability determined by coupling strengths and topology on complex networks,” Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, vol. 75, no. 6, Article ID 066106, 11 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  7. G.-P. Jiang, W. K.-S. Tang, and G. Chen, “A state-observer-based approach for synchronization in complex dynamical networks,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 53, no. 12, pp. 2739–2745, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  8. J. Wu and L. Jiao, “Observer-based synchronization in complex dynamical networks with nonsymmetric coupling,” Physica A. Statistical Mechanics and Its Applications, vol. 386, pp. 469–480, 2007.
  9. X. F. Wang and G. Chen, “Pinning control of scale-free dynamical networks,” Physica A. Statistical Mechanics and Its Applications, vol. 310, no. 3-4, pp. 521–531, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. X. Li, X. F. Wang, and G. Chen, “Pinning a complex dynamical network to its equilibrium,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 51, no. 10, pp. 2074–2087, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  11. M. Porfiri and M. di Bernardo, “Criteria for global pinning-controllability of complex networks,” Automatica, vol. 44, no. 12, pp. 3100–3106, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. W. Yu, G. Chen, and J. Lü, “On pinning synchronization of complex dynamical networks,” Automatica, vol. 45, no. 2, pp. 429–435, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. T. Chen, X. Liu, and W. Lu, “Pinning complex networks by a single controller,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 54, no. 6, pp. 1317–1326, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. Lu, D. W. C. Ho, and Z. Wang, “Pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers,” IEEE Transactions on Neural Networks, vol. 20, no. 10, pp. 1617–1629, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. Q. Song and J. Cao, “On pinning synchronization of directed and undirected complex dynamical networks,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 57, no. 3, pp. 672–680, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  16. H. S. Su and X. F. Wang, Pinning Control of Complex Networked Systems: Synchronization, Consensus and Flocking of Networked Systems via Pinning, Springer, Shanghai Jiaotong University Press, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  17. H. S. Su, Z. Rong, M. Z. Q. Chen, X. F. Wang, G. Chen, and H. Wang, “Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks,” IEEE Transactions on Cybernetics, vol. 43, no. 1, pp. 394–399, 2013.
  18. Q. Song, F. Liu, J. Cao, and W. Yu, “Pinning-controllability analysis of complex networks: an M-matrix approach,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 59, no. 11, pp. 2692–2701, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. Q. Song, F. Liu, J. Cao, and W. Yu, “M-matrix strategies for pinning-controlled leader-following consensus in multiagent systems with nonlinear dynamics,” IEEE Transactions on Cybernetics, vol. 43, no. 6, pp. 1688–1697, 2013.
  20. G. Wen, Z. Duan, G. Chen, and W. Yu, “Consensus tracking of multi-agent systems with Lipschitz-type node dynamics and switching topologies,” IEEE Transactions on Circuits and Systems. I: Regular Papers, vol. 61, no. 2, pp. 499–511, 2014.
  21. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  22. Z. Li, Z. Duan, and G. Chen, “Global synchronised regions of linearly coupled Lur'e systems,” International Journal of Control, vol. 84, no. 2, pp. 216–227, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. Q. Song, F. Liu, J. Cao, and J. Lu, “Some simple criteria for pinning a Lur'e network with directed topology,” IET Control Theory and Applications, vol. 8, no. 2, pp. 131–138, 2014.
  24. G.-D. Hu, “Observers for one-sided Lipschitz non-linear systems,” IMA Journal of Mathematical Control and Information, vol. 23, no. 4, pp. 395–401, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  25. Y. Zhao, J. Tao, and N.-Z. Shi, “A note on observer design for one-sided Lipschitz nonlinear systems,” Systems & Control Letters, vol. 59, no. 1, pp. 66–71, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. W. Zhang, H.-S. Su, Y. Liang, and Z.-Z. Han, “Non-linear observer design for one-sided Lipschitz systems: an linear matrix inequality approach,” IET Control Theory & Applications, vol. 6, no. 9, pp. 1297–1303, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  27. J. Löfberg, “YALMIP: a toolbox for modeling and optimization in MATLAB,” in Proceedings of the IEEE International Symposium on Computer Aided Control System Design, pp. 284–289, Taipei, Taiwan, September 2004. View at Scopus
  28. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet