About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 587426, 16 pages
http://dx.doi.org/10.1155/2012/587426
Research Article

Delay-Dependent Guaranteed Cost Controller Design for Uncertain Neural Networks with Interval Time-Varying Delay

1Major of Mathematics and Statistics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand
2Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50000, Thailand

Received 3 August 2012; Revised 24 September 2012; Accepted 25 September 2012

Academic Editor: Xiaodi Li

Copyright © 2012 M. Rajchakit 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. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proceedings of the National Academy of Sciences of the United States of America, vol. 79, no. 8, pp. 2554–2558, 1982. View at Publisher · View at Google Scholar
  2. G. Kevin, An Introduction to Neural Networks, CRC Press, 1997.
  3. M. Wu, Y. He, and J.-H. She, Stability Analysis and Robust Control of Time-Delay Systems, Springer, 2010. View at Publisher · View at Google Scholar
  4. S. Arik, “An improved global stability result for delayed cellular neural networks,” IEEE Transactions on Circuits and Systems I, vol. 49, no. 8, pp. 1211–1214, 2002. View at Publisher · View at Google Scholar
  5. K. Ratchagit, “Asymptotic stability of delay-difference system of Hopfield neural networks via matrix inequalities and application,” International Journal of Neural Systems, vol. 17, pp. 425–430, 2007.
  6. Y. He, Q.-G. Wang, and M. Wu, “LMI-based stability criteria for neural networks with multiple time-varying delays,” Physica D, vol. 212, no. 1-2, pp. 126–136, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. O. M. Kwon and J. H. Park, “Exponential stability analysis for uncertain neural networks with interval time-varying delays,” Applied Mathematics and Computation, vol. 212, no. 2, pp. 530–541, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. V. N. Phat and H. Trinh, “Exponential stabilization of neural networks with various activation functions and mixed time-varying delays,” IEEE Transactions on Neural Networks, vol. 21, pp. 1180–1185, 2010.
  9. W.-H. Chen, Z.-H. Guan, and X. Lu, “Delay-dependent output feedback guaranteed cost control for uncertain time-delay systems,” Automatica, vol. 40, no. 7, pp. 1263–1268, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. M. N. Parlakçí, “Robust delay-dependent guaranteed cost controller design for uncertain neutral systems,” Applied Mathematics and Computation, vol. 215, no. 8, pp. 2936–2949, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. J. H. Park and O. Kwon, “On guaranteed cost control of neutral systems by retarded integral state feedback,” Applied Mathematics and Computation, vol. 165, no. 2, pp. 393–404, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J. H. Park and K. Choi, “Guaranteed cost control for uncertain nonlinear neutral systems via memory state feedback,” Chaos, Solitons and Fractals, vol. 24, no. 1, pp. 183–190, 2005. View at Publisher · View at Google Scholar
  13. J. H. Park and O. M. Kwon, “Guaranteed cost control of time-delay chaotic systems,” Chaos, Solitons and Fractals, vol. 27, no. 4, pp. 1011–1018, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. J. H. Park, “Dynamic output guaranteed cost controller for neutral systems with input delay,” Chaos, Solitons and Fractals, vol. 23, no. 5, pp. 1819–1828, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. J. H. Park, “Delay-dependent criterion for guaranteed cost control of neutral delay systems,” Journal of Optimization Theory and Applications, vol. 124, no. 2, pp. 491–502, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. J. H. Park, “A novel criterion for global asymptotic stability of BAM neural networks with time delays,” Chaos, Solitons and Fractals, vol. 29, no. 2, pp. 446–453, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. H. Park, “On global stability criterion for neural networks with discrete and distributed delays,” Chaos, Solitons and Fractals, vol. 30, no. 4, pp. 897–902, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. H. He, L. Yan, and J. Tu, “Guaranteed cost stabilization of time-varying delay cellular neural networks via Riccati inequality approach,” Neural Processing Letters, vol. 35, pp. 151–158, 2012.
  19. J. Tu and H. He, “Guaranteed cost synchronization of chaotic cellular neural networks with time-varying delay,” Neural Computation, vol. 24, no. 1, pp. 217–233, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. J. Tu, H. He1, and P. Xiong, “Guaranteed cost synchronous control of time-varying delay cellular neural networks,” Neural Computing and Applications. View at Publisher · View at Google Scholar
  21. H. He and J. Tu, “Algebraic condition of synchronization for multiple time-delayed chaotic Hopfield neural networks,” Neural Computing and Applications, vol. 19, pp. 543–548, 2010.
  22. H. He, J. Tu, and P. Xiong, “Lr-synchronization and adaptive synchronization of a class of chaotic Lurie systems under perturbations,” Journal of the Franklin Institute, vol. 348, no. 9, pp. 2257–2269, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. E. Fridman and Y. Orlov, “Exponential stability of linear distributed parameter systems with time-varying delays,” Automatica, vol. 45, no. 1, pp. 194–201, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. S. Xu and J. Lam, “A survey of linear matrix inequality techniques in stability analysis of delay systems,” International Journal of Systems Science, vol. 39, no. 12, pp. 1095–1113, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. J.-S. Xie, B.-Q. Fan, Y. S. Lee, and J. Yang, “Guaranteed cost controller design of networked control systems with state delay,” Acta Automatica Sinica, vol. 33, no. 2, pp. 170–174, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. L. Yu and F. Gao, “Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays,” Journal of the Franklin Institute, vol. 338, no. 1, pp. 101–110, 2001. View at Publisher · View at Google Scholar
  27. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15, SIAM, Philadelphia, Pa, USA, 1994. View at Publisher · View at Google Scholar
  28. K. Gu, V. Kharitonov, and J. Chen, Stability of Time-delay Systems, Birkhauser, Berlin, Germany, 2003.