Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2011, Article ID 138912, 20 pages
http://dx.doi.org/10.1155/2011/138912
Research Article

Robust Stability Criteria for Uncertain Neutral Systems with Interval Nondifferentiable Time-Varying Delay and Nonlinear Perturbations

W. Weera1,2 and P. Niamsup1,2

1Department of Mathematics, Chiang Mai University, Chiang Mai 50200, Thailand
2Center of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 7 July 2011; Accepted 13 September 2011

Academic Editor: James Buchanan

Copyright © 2011 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. J. Zhang, P. Shi, and J. Qiu, “Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties,” Chaos, Solitons and Fractals, vol. 38, no. 1, pp. 160–167, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. C.-C. Shen and S.-M. Zhong, “New delay-dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2277–2285, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. K.-W. Yu and C.-H. Lien, “Stability criteria for uncertain neutral systems with interval time-varying delays,” Chaos, Solitons and Fractals, vol. 38, no. 3, pp. 650–657, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. O. M. Kwon, J. H. Park, and S. M. Lee, “On delay-dependent robust stability of uncertain neutral systems with interval time-varying delays,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 843–853, 2008. View at Publisher · View at Google Scholar
  5. Q.-L. Han and L. Yu, “Robust stability of linear neutral systems with nonlinear parameter perturbations,” IEE Proceedings, vol. 151, no. 5, pp. 539–546, 2004. View at Publisher · View at Google Scholar
  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. Y.-Y. Cao and J. Lam, “Computation of robust stability bounds for time-delay systems with nonlinear time-varying perturbations,” International Journal of Systems Science, vol. 31, no. 3, pp. 359–365, 2000. View at Publisher · View at Google Scholar
  8. J. Cao and J. Wang, “Delay-dependent robust stability of uncertain nonlinear systems with time delay,” Applied Mathematics and Computation, vol. 154, no. 1, pp. 289–297, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. Q.-L. Han, “Robust stability for a class of linear systems with time-varying delay and nonlinear perturbations,” Computers & Mathematics with Applications, vol. 47, no. 8-9, pp. 1201–1209, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. X. Jiang and Q.-L. Han, “Delay-dependent robust stability for uncertain linear systems with interval time-varying delay,” Automatica, vol. 42, no. 6, pp. 1059–1065, 2006. View at Publisher · View at Google Scholar
  11. 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 · View at Zentralblatt MATH
  12. 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
  13. 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
  14. 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
  15. V. N. Phat and P. Niamsup, “Stability of linear time-varying delay systems and applications to control problems,” Journal of Computational and Applied Mathematics, vol. 194, no. 2, pp. 343–356, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. R. Rakkiyappan, P. Balasubramaniam, and R. Krishnasamy, “Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2147–2156, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay System, Birkhauser, Boston, Mass, USA, 2003.
  18. Z. Zuo and Y. Wang, “New stability criterion for a class of linear systems with time-varying delay and nonlinear perturbations,” IEE Proceedings, vol. 153, no. 5, pp. 623–626, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. T.-F. Li and Z.-D. Xu, “Robust stability criteria of neutral systems with time varying delay and nonlinear uncertainties,” in Proceedings of the Chinese Control and Decision Conference (CCDC '09), pp. 4056–4060, 2009. View at Publisher · View at Google Scholar