Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2009 (2009), Article ID 294845, 18 pages
http://dx.doi.org/10.1155/2009/294845
Research Article

Improved Robust Stability Criteria of Uncertain Neutral Systems with Mixed Delays

1School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China
2School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang 550004, China
3School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China

Received 1 March 2009; Revised 5 August 2009; Accepted 1 September 2009

Academic Editor: Wolfgang Ruess

Copyright © 2009 Zixin 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. Q.-L. Han, “A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems,” Automatica, vol. 44, no. 1, pp. 272–277, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. 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
  3. D.-Y. Chen and C.-Y. Jin, “Delay-dependent stability criteria for a class of uncertain neutral systems,” Acta Automatica Sinica, vol. 34, no. 8, pp. 989–992, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  4. M. Li and L. Liu, “A delay-dependent stability criterion for linear neutral delay systems,” Journal of the Franklin Institute, vol. 346, no. 1, pp. 33–37, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J. H. Park and S. Won, “A note on stability of neutral delay-differential systems,” Journal of the Franklin Institute, vol. 336, no. 3, pp. 543–548, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. H. Park and S. Won, “Asymptotic stability of neutral systems with multiple delays,” Journal of Optimization Theory and Applications, vol. 103, no. 1, pp. 183–200, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. O. M. Kwon, J. H. Park, and S. M. Lee, “Augmented Lyapunov functional approach to stability of uncertain neutral systems with time-varying delays,” Applied Mathematics and Computation, vol. 207, no. 1, pp. 202–212, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  8. O. M. Kwon, J. H. Park, and S. M. Lee, “On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays,” Applied Mathematics and Computation, vol. 197, no. 2, pp. 864–873, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. Tian, L. Xiong, J. Liu, and X. Xie, “Novel delay-dependent robust stability criteria for uncertain neutral systems with time-varying delay,” Chaos, Solitons & Fractals, vol. 40, no. 4, pp. 1858–1866, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  10. B. Wang, X. Liu, and S. Zhong, “New stability analysis for uncertain neutral system with time-varying delay,” Applied Mathematics and Computation, vol. 197, no. 1, pp. 457–465, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. X. Li and X. Zhu, “Stability analysis of neutral systems with distributed delays,” Automatica, vol. 44, pp. 2197–2201, 2008. View at Google Scholar
  12. D. Liu, S. Zhong, and L. Xiong, “On robust stability of uncertain neutral systems with multiple delays,” Chaos, Solitons & Fractals, vol. 39, no. 5, pp. 2332–2339, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  13. L. Xiong, S. Zhong, and J. Tian, “Novel robust stability criteria of uncertain neutral systems with discrete and distributed delays,” Chaos, Solitons & Fractals, vol. 40, no. 2, pp. 771–777, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  14. 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 · View at MathSciNet
  15. X. Li, X. Zhu, and A. Cela, “Stability analysis of neutral systems with mixed delays,” Automatica, vol. 11, pp. 2968–2972, 2008. View at Google Scholar
  16. H. Li, H. Li, and S. Zhong, “Stability of neutral type descriptor system with mixed delays,” Chaos, Solitons & Fractals, vol. 33, no. 5, pp. 1796–1800, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. 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, pp. 1549–1556, 2007. View at Google Scholar
  18. Q. Zhang, X. Wei, and J. Xu, “A generalized LMI-based approach to the global asymptotic stability of discrete-time delayed recurrent neural networks,” International Journal of Innovative Computing, Information and Control, vol. 4, pp. 1393–1400, 2008. View at Google Scholar
  19. E. Boukas, “Free-weighting matrices delay-dependent stabilization for systems with time-varying delays,” ICIC Express Letters, vol. 2, pp. 167–173, 2008. View at Google Scholar
  20. L. Xia, M. Xia, and L. Liu, “LMI conditions for global asymptotic stability of neural networks with discrete and distributed delays,” ICIC Express Letters, vol. 2, pp. 257–262, 2008. View at Google Scholar
  21. T. Mori, “Criteria for asymptotic stability of linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 30, no. 2, pp. 158–161, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. 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, SIAM, Philadelphia, Pa, USA, 1994. View at MathSciNet
  23. L. Xie, “Output feedback H control of systems with parameter uncertainty,” International Journal of Control, vol. 63, no. 4, pp. 741–750, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. J. Yan, “Robust stability analysis of uncertain time delay systems with delay-dependence,” Electronics Letters, vol. 37, pp. 135–137, 2001. View at Google Scholar
  25. 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 · View at MathSciNet
  26. K.-K. Fan, J.-D. Chen, C.-H. Lien, and J.-G. Hsieh, “Delay-dependent stability criterion for neutral time-delay systems via linear matrix inequality approach,” Journal of Mathematical Analysis and Applications, vol. 273, no. 2, pp. 580–589, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. C. Lien and J. Chen, “Discrete-delay-independent and discrete-delay-dependent criteria for a class of neutral systems,” Journal of Dynamic Systems, Measurement, and Control, vol. 125, pp. 33–41, 2003. View at Google Scholar
  28. J. 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
  29. C.-H. Lien, K.-W. Yu, and J.-G. Hsieh, “Stability conditions for a class of neutral systems with multiple time delays,” Journal of Mathematical Analysis and Applications, vol. 245, no. 1, pp. 20–27, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. S. Neculescu, “Further remarks on delay-dependent stability of linear neutral system,” in Proceedings of the International Symposium on Mathematical Theory of Networks and Systems (MTNS '00), Perpignan, France, 2000.
  31. 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 Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. 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 Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. Q.-L. Han, “On stability of linear neutral systems with mixed time delays: a discretized Lyapunov functional approach,” Automatica, vol. 41, no. 7, pp. 1209–1218, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. J. H. Park, O. M. Kwon, and S. M. Lee, “LMI optimization approach on stability for delayed neural networks of neutral-type,” Applied Mathematics and Computation, vol. 196, no. 1, pp. 236–244, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  35. K. Gu, “A further refinement of discretized Lyapunov functional method for the stability of time-delay systems,” International Journal of Control, vol. 74, no. 10, pp. 967–976, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. Q.-L. Han, “Robust stability of uncertain delay-differential systems of neutral type,” Automatica, vol. 38, no. 4, pp. 719–723, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet