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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 961382, 18 pages
http://dx.doi.org/10.1155/2012/961382
Research Article

Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type

W. Weera1 and P. Niamsup1,2,3

1Department of Mathematics, Chiang Commission of Higher Education Mai University, Chiang Mai 50200, Thailand
2Center of Excellence in Mathematics, (CHE), Si Ayutthaya Road, Bangkok 10400, Thailand
3Materials Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 16 September 2012; Accepted 22 November 2012

Academic Editor: Ivanka Stamova

Copyright © 2012 W. Weera and P. Niamsup. 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. I. Amri, D. Soudani, and M. Benrejeb, “Delay dependent robust exponential stability criterion for perturbed and uncertain neutral systems with time varying delays,” Studies in Informatics and Control, vol. 19, no. 2, pp. 135–144, 2010. View at Scopus
  2. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay System, Birkhäauser, Boston, Mass, USA, 2003.
  3. O. M. Kwon and J. H. Park, “Exponential stability for time-delay systems with interval time-varying delays and nonlinear perturbations,” Journal of Optimization Theory and Applications, vol. 139, no. 2, pp. 277–293, 2008. View at Publisher · View at Google Scholar
  4. O. M. Kwon, J. H. Park, and S. M. Lee, “On robust stability criterion for dynamic systems with time-varying delays and nonlinear perturbations,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 937–942, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J. H. Park, “Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations,” Applied Mathematics and Computation, vol. 161, no. 2, pp. 413–421, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. F. Qiu, B. Cui, and Y. Ji, “Further results on robust stability of neutral system with mixed time-varying delays and nonlinear perturbations,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 895–906, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. S. Lakshmanan, T. Senthilkumar, and P. Balasubramaniam, “Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations,” Applied Mathematical Modelling, vol. 35, no. 11, pp. 5355–5368, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. J. Gao, H. Su, X. Ji, and J. Chu, “Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity,” Nonlinear Analysis: Real World Applications, vol. 9, no. 5, pp. 2350–2360, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. K. Ramakrishnan and G. Ray, “Improved delay-range-dependent robust stability criteria for a class of Lur'e systems with sector-bounded nonlinearity,” Journal of Computational and Applied Mathematics, vol. 235, pp. 2147–2156, 2011.
  10. H. K. Khalil, Nonlinear Systems, Prentice-Hall, Upper Saddle River, NJ, USA, 1996.
  11. X. X. Liao, Absolute Stability of Nonlinear Control Systems, vol. 5 of Mathematics and Its Applications (Chinese Series), Kluwer Academic, Dordrecht, The Netherlands, 1993.
  12. V.-M. Popov, Hyperstability of Control Systems, Editura Academiei, Bucharest, Romania, 1973.
  13. T. Botmart, P. Niamsup, and V. N. Phat, “Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays,” Applied Mathematics and Computation, vol. 217, no. 21, pp. 8236–8247, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. K.-W. Yu and C.-H. Lien, “Stability criteria for uncertain neutral systems with interval time-varying delays,” Chaos, Solitons & Fractals, vol. 38, no. 3, pp. 650–657, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. B. Chen and J. Wang, “Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time-varying delays,” Neural Networks, vol. 20, no. 10, pp. 1067–1080, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. Q.-L. Han, A. Xue, S. Liu, and X. Yu, “Robust absolute stability criteria for uncertain Lur'e systems of neutral type,” International Journal of Robust and Nonlinear Control, vol. 18, no. 3, pp. 278–295, 2008. View at Publisher · View at Google Scholar
  17. C. Yin, S.-m. Zhong, and W.-F. Chen, “On delay-dependent robust stability of a class of uncertain mixed neutral and Lur'e dynamical systems with interval time-varying delays,” Journal of the Franklin Institute, vol. 347, no. 9, pp. 1623–1642, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. R. Samidurai, S. M. Anthoni, and K. Balachandran, “Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays,” Nonlinear Analysis: Hybrid Systems, vol. 4, no. 1, pp. 103–112, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. H. Wu, Y. Zhong, and H. Mai, “On delay-dependent exponential stability of neutral-type neural networks with interval time-varying delays,” in Proceedings of the International Conference on Artificial Intelligence and Computational Intelligence (AICI '09), vol. 2, pp. 563–569, Shanghai, China, November 2009. View at Publisher · View at Google Scholar
  20. G. Liu and S. X. Yang, “Stability criterion for BAM neural networks of neutral-type with interval time-varying delays,” Procedia Engineering, vol. 15, pp. 2836–2840, 2011.
  21. Z. Zhang, K. Liu, and Y. Yang, “New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type,” Neurocomputing, vol. 81, pp. 24–32, 2012. View at Publisher · View at Google Scholar