Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2008, Article ID 761342, 9 pages
http://dx.doi.org/10.1155/2008/761342
Research Article

Sliding Mode Control of Uncertain Neutral Stochastic Systems with Multiple Delays

1Department of Automation, Shanghai Jiaotong University, Shanghai 200030, China
2Department of Mathematics, Shanghai Maritime University, Shanghai 200135, China

Received 31 August 2007; Accepted 4 March 2008

Academic Editor: Paulo Gonçalves

Copyright © 2008 Dilan Chen and Weidong Zhang. 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. M. S. Mahmoud, Robust Control and Filtering for Time-Delay Systems, vol. 5 of Control Engineering, Marcel Dekker, New York, NY, USA, 2000. View at Zentralblatt MATH · View at MathSciNet
  2. J. Sun, “Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control,” Chaos, Solitons & Fractals, vol. 21, no. 1, pp. 143–150, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. Cao, “Global stability conditions for delayed CNNs,” IEEE Transactions on Circuits and Systems I, vol. 48, no. 11, pp. 1330–1333, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. K. Zhang, “Stability analysis of linear neutral systems with multiple time delays,” Mathematical Problems in Engineering, vol. 2005, no. 2, pp. 175–183, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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
  6. F. Ren and J. Cao, “Novel α-stability criterion of linear systems with multiple time delays,” Applied Mathematics and Computation, vol. 181, no. 1, pp. 282–290, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  7. E.-K. Boukas, Stochastic Hybrid Systems: Analysis and Design, Birkhäuser, Boston, Mass, USA, 2005.
  8. D. Ya. Khusainov, “Investigation of interval stability of linear systems of neutral type of Lyapunov function method,” Journal of Applied Mathematics and Stochastic Analysis, vol. 15, no. 1, pp. 71–81, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. Li, H.-B. Li, and S.-M. 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 MathSciNet
  10. M. S. Mahmoud and L. Xie, “Passivity analysis and synthesis for uncertain time-delay systems,” Mathematical Problems in Engineering, vol. 7, no. 5, pp. 455–484, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. B. Lee and J. G. Lee, “Robust stability and stabilization of linear delayed systems with structured uncertainty,” Automatica, vol. 35, no. 6, pp. 1149–1154, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. W. Yu and J. Cao, “Robust control of uncertain stochastic recurrent neural networks with time-varying delay,” Neural Processing Letters, vol. 26, no. 2, pp. 101–119, 2007. View at Publisher · View at Google Scholar
  13. C. Edwards and S. K. Spurgeon, Sliding Mode Control: Theory and Applictions, Taylor & Francis, New York, NY, USA, 1998.
  14. Y. Niu, D. W. C. Ho, and J. Lam, “Robust integral sliding mode control for uncertain stochastic systems with time-varying delay,” Automatica, vol. 41, no. 5, pp. 873–880, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Boutat-Baddas, J. P. Barbot, D. Boutat, and R. Tauleigne, “Sliding mode observers and observability singularity in chaotic synchronization,” Mathematical Problems in Engineering, vol. 2004, no. 1, pp. 11–31, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet