Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2009, Article ID 759248, 22 pages
http://dx.doi.org/10.1155/2009/759248
Research Article

New Delay-Dependent Stability Criteria for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

Institute of Informatics and Applications, University of Girona, Campus de Montilivi, Edifici P4, 17071 Girona, Spain

Received 19 July 2008; Revised 8 November 2008; Accepted 1 January 2009

Academic Editor: Shijun Liao

Copyright © 2009 Hamid Reza Karimi 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. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1993. View at Zentralblatt MATH · View at MathSciNet
  2. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems, Birkhäuser, Boston, Mass, USA, 2003. View at Zentralblatt MATH
  3. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993. View at Zentralblatt MATH · View at MathSciNet
  4. Y. Wang, L. Xie, and C. E. de Souza, “Robust control of a class of uncertain nonlinear systems,” Systems & Control Letters, vol. 19, no. 2, pp. 139–149, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. R. Karimi, “A computational method for optimal control problem of time-varying state-delayed systems by Haar wavelets,” International Journal of Computer Mathematics, vol. 83, no. 2, pp. 235–246, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Y. He, Q.-G. Wang, L. Xie, and C. Lin, “Further improvement of free-weighting matrices technique for systems with time-varying delay,” IEEE Transactions on Automatic Control, vol. 52, no. 2, pp. 293–299, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  7. Q.-L. Han, “A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays,” Automatica, vol. 40, no. 10, pp. 1791–1796, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. E. Fridman, “New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems,” Systems & Control Letters, vol. 43, no. 4, pp. 309–319, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Q.-L. Han and L. Yu, “Robust stability of linear neutral systems with nonlinear parameter perturbations,” IEE Proceedings: Control Theory and Applications, vol. 151, no. 5, pp. 539–546, 2004. View at Publisher · View at Google Scholar
  10. 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, pp. 1201–1209, 2004. View at Google Scholar · View at MathSciNet
  11. P. Park, “A delay-dependent stability criterion for systems with uncertain time-invariant delays,” IEEE Transactions on Automatic Control, vol. 44, no. 4, pp. 876–877, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee, “Delay-dependent robust stabilization of uncertain state-delayed systems,” International Journal of Control, vol. 74, no. 14, pp. 1447–1455, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Ju. H. Park and O. Kwon, “On new stability criterion for delay-differential systems of neutral type,” Applied Mathematics and Computation, vol. 162, no. 2, pp. 627–637, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Y. He, Q.-G. Wang, C. Lin, and M. Wu, “Delay-range-dependent stability for systems with time-varying delay,” Automatica, vol. 43, no. 2, pp. 371–376, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Q.-L. Han, X. Yu, and K. Gu, “On computing the maximum time-delay bound for stability of linear neutral systems,” IEEE Transactions on Automatic Control, vol. 49, no. 12, pp. 2281–2285, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  16. 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 · View at Zentralblatt MATH · View at MathSciNet
  17. J. Lam, H. Gao, and C. Wang, “H model reduction of linear systems with distributed delay,” IEE Proceedings: Control Theory and Applications, vol. 152, no. 6, pp. 662–674, 2005. View at Publisher · View at Google Scholar
  18. 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 Google Scholar · View at Zentralblatt MATH
  19. Y. Chen, A. Xue, R. Lu, and S. Zhou, “On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 8, pp. 2464–2470, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. M. N. A. Parlakçı, “Delay-dependent robust stability criteria for uncertain neutral systems with mixed time-varying discrete and neutral delays,” Asian Journal of Control, vol. 9, no. 4, pp. 411–421, 2007. View at Google Scholar · View at MathSciNet
  21. J. Zhang, P. Shi, and J. Qiu, “Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties,” Chaos, Solitons & Fractals, vol. 38, no. 1, pp. 160–167, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. 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 & Fractals, 2007. View at Publisher · View at Google Scholar
  23. Y. He, G.-P. Liu, D. Rees, and M. Wu, “Improved delay-dependent stability criteria for systems with nonlinear perturbations,” European Journal of Control, vol. 13, no. 4, pp. 356–365, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  24. B. Yang, J. Wang, X. Pan, and C. Zhong, “Delay-dependent criteria for robust stability of linear neutral systems with time-varying delay and nonlinear perturbations,” International Journal of Systems Science, vol. 38, no. 6, pp. 511–518, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. Y. Chen and W. Su, “New robust stability of cellular neural networks with time-varying discrete and distributed delays,” International Journal of Innovative Computing, Information and Control, vol. 3, no. 6B, pp. 1549–1556, 2007. View at Google Scholar
  26. W.-H. Chen and W. X. Zheng, “Delay-dependent robust stabilization for uncertain neutral systems with distributed delays,” Automatica, vol. 43, no. 1, pp. 95–104, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. Z. Zuo and Y. Wang, “New stability criterion for a class of linear systems with time-varying delay and nonlinear perturbations,” IEE Proceedings: Control Theory and Applications, vol. 153, no. 5, pp. 623–626, 2006. View at Google Scholar · View at MathSciNet
  28. J. D. Chen, C. H. Lien, K. K. Fan, and J. H. Chou, “Criteria for asymptotic stability of a class of neutral systems viaa LMI approach,” IEE Proceedings: Control Theory and Applications, vol. 148, no. 6, pp. 442–447, 2001. View at Publisher · View at Google Scholar
  29. J. D. Chen, “LMI-based robust H control of uncertain neutral systems with state and input delays,” Journal of Optimization Theory and Applications, vol. 126, no. 3, pp. 553–570, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. H. R. Karimi, P. J. Maralani, B. Lohmann, and B. Moshiri, “H control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions,” International Journal of Control, vol. 78, no. 4, pp. 254–263, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. M. Basin, J. Perez, and D. Calderon-Alvarez, “Optimal filtering for linear systems over polynomial observations,” International Journal of Innovative Computing, Information and Control, vol. 4, no. 2, pp. 313–320, 2008. View at Google Scholar
  32. M. Basin, E. Sanchez, and R. Martinez-Zuniga, “Optimal linear filtering for systems with multiple state and observation delays,” International Journal of Innovative Computing, Information and Control, vol. 3, no. 5, pp. 1309–1320, 2007. View at Google Scholar
  33. S. Xu, J. Lam, and C. Yang, “H and positive-real control for linear neutral delay systems,” IEEE Transactions on Automatic Control, vol. 46, no. 8, pp. 1321–1326, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. H. R. Karimi, M. Zapateiro, and N. Luo, “Robust mixed H2/H delayed state feedback control of uncertain neutral systems with time-varying delays,” Asian Journal of Control, vol. 10, no. 5, pp. 569–580, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  35. H. R. Karimi, “Observer-based mixed H2/H control design for linear systems with time-varying delays: an LMI approach,” International Journal of Control, Automation and Systems, vol. 6, no. 1, pp. 1–14, 2008. View at Google Scholar
  36. H. R. Karimi and H. Gao, “LMI-based delay-dependent mixed H2/H control of second-order neutral systems with time-varying state and input delays,” ISA Transactions, vol. 47, no. 3, pp. 311–324, 2008. View at Google Scholar
  37. B. Chen, J. Lam, and S. Xu, “Memory state feedback guaranteed cost control for neutral systems,” International Journal of Innovative Computing, Information and Control, vol. 2, no. 2, pp. 293–303, 2006. View at Google Scholar
  38. Ju. H. Park, “Dynamic output guaranteed cost controller for neutral systems with input delay,” Chaos, Solitons & Fractals, vol. 23, no. 5, pp. 1819–1828, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  39. M. S. Mahmoud, Y. Shi, and H. N. Nounou, “Resilient observer-based control of uncertain time-delay systems,” International Journal of Innovative Computing, Information and Control, vol. 3, no. 2, pp. 407–418, 2007. View at Google Scholar
  40. D. D. Šiljak and D. M. Stipanović, “Robust stabilization of nonlinear systems: the LMI approach,” Mathematical Problems in Engineering, vol. 6, no. 5, pp. 461–493, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  41. Z. Zuo, J. Wang, and L. Huang, “Robust stabilization for non-linear discrete-time systems,” International Journal of Control, vol. 77, no. 4, pp. 384–388, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  42. Y. He, M. Wu, J.-H. She, and G.-P. Liu, “Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays,” Systems & Control Letters, vol. 51, no. 1, pp. 57–65, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  43. X. He, Z. Wang, and D. Zhou, “Robust H filtering for networked systems with multiple state delays,” International Journal of Control, vol. 80, no. 8, pp. 1217–1232, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  44. H. Gao, T. Chen, and J. Lam, “A new delay system approach to network-based control,” Automatica, vol. 44, no. 1, pp. 39–52, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  45. P. P. Khargonekar, I. R. Petersen, and K. Zhou, “Robust stabilization of uncertain linear systems: quadratic stabilizability and H control theory,” IEEE Transactions on Automatic Control, vol. 35, no. 3, pp. 356–361, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  46. O. M. Kwon and Ju. H. Park, “Exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 813–823, 2008. View at Publisher · View at Google Scholar · View at MathSciNet