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Journal of Control Science and Engineering
Volume 2012, Article ID 517157, 12 pages
http://dx.doi.org/10.1155/2012/517157
Research Article

State Feedback Stabilization for Neutral-Type Neural Networks with Time-Varying Discrete and Unbounded Distributed Delays

School of Mathematical Science, Heilongjiang University, Harbin 150080, China

Received 19 December 2011; Revised 27 March 2012; Accepted 21 April 2012

Academic Editor: Onur Toker

Copyright © 2012 Yantao Wang 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. W. S. McCulloch and W. Pitts, “A logical calculus of the ideas immanent in nervous activity,” The Bulletin of Mathematical Biophysics, vol. 5, no. 4, pp. 115–133, 1943. View at Publisher · View at Google Scholar · View at Scopus
  2. J. Li, “New delay-dependent robust stability condition for neutral-type neural networks with mixed time delays,” in Procedings of the 2nd International Conference on Industrial Mechatronics and Automation (ICIMA '10), vol. 1, pp. 486–489, May 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. M. S. Mahmoud and A. Ismail, “Improved results on robust exponential stability criteria for neutral-type delayed neural networks,” Applied Mathematics and Computation, vol. 217, no. 7, pp. 3011–3019, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. Sun and J. Cao, “Stabilization of stochastic delayed neural networks with markovian switching,” Asian Journal of Control, vol. 10, no. 3, pp. 327–340, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. J. F. Wang, J. G. Jian, and P. Yan, “Finite-time boundedness analysis of a class of neutral type neural networks with time delays,” in Proceedings of the 6th International Symposium on Neural Networks on Advances in Neural Networks, vol. 1, pp. 395–404, 2009.
  6. J. Liu and G. Zong, “New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type,” Neurocomputing, vol. 72, no. 10–12, pp. 2549–2555, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. Q. Zhang, X. Wei, and J. Xu, “Global exponential stability for nonautonomous cellular neural networks with unbounded delays,” Chaos, Solitons and Fractals, vol. 39, no. 3, pp. 1144–1151, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. H. Yang and T. Chu, “LMI conditions for stability of neural networks with distributed delays,” Chaos, Solitons and Fractals, vol. 34, no. 2, pp. 557–563, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. B. Song, S. Xu, and Y. Zou, “Delay-dependent robust H filtering for uncertain neutral stochastic time-delay systems,” Circuits, Systems, and Signal Processing, vol. 28, no. 2, pp. 241–256, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. Li, S. Xu, B. Zhang, and Y. Chu, “Delay-dependent guaranteed cost control for uncertain neutral systems with distributed delays,” International Journal of Control, Automation and Systems, vol. 6, no. 1, pp. 15–23, 2008. View at Google Scholar · View at Scopus
  11. Y. Chen, W. X. Zheng, and A. Xue, “A new result on stability analysis for stochastic neutral systems,” Automatica, vol. 46, no. 12, pp. 2100–2104, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. P. Balasubramaniam, A. Manivannan, and R. Rakkiyappan, “Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters,” Applied Mathematics and Computation, vol. 216, no. 11, pp. 3396–3407, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Wang, Y. He, and X. Zhang, “Refined delay-dependent robust stability criteria of a class of uncertain mixed neutral and lur'e dynamical systems with interval time-varying,” in Proceedings of the Chinese Control and Decision Conference (CCDC '11), pp. 4179–4184, Sichuan, China, May 2011. View at Publisher · View at Google Scholar
  14. T. Yi, G. Liu, Y. Liu, and R. Wang, “Global robust stability analysis for uncertain stochastic neural networks of neutral-type with time-varying delays,” in Proceedings of the International Conference on Electric Information and Control Engineering (ICEICE '11), pp. 1399–1403, April 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Chen, Y. Zhang, and P. Hu, “Novel delay-dependent robust stability criteria for neutral stochastic delayed neural networks,” Neurocomputing, vol. 73, no. 13–15, pp. 2554–2561, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. W. Su and Y. Chen, “Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1576–1581, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. L. Jin, “New LMI-based stability condition for neutral-type neural networks with variable and distributed delays,” in Proceedings of the International Conference on Intelligent System Design and Engineering Application (ISDEA '10), pp. 1002–1005, October 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. J. E. Feng, S. Xu, and Y. Zou, “Delay-dependent stability of neutral type neural networks with distributed delays,” Neurocomputing, vol. 72, no. 10-12, pp. 2576–2580, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. X. Li, “Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4370–4384, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. R. Rakkiyappan and P. Balasubramaniam, “New global exponential stability results for neutral type neural networks with distributed time delays,” Neurocomputing, vol. 71, no. 4–6, pp. 1039–1045, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. R. Rakkiyappan and P. Balasubramaniam, “LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays,” Applied Mathematics and Computation, vol. 204, no. 1, pp. 317–324, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. C. Y. Lu, “A delay-dependent approach to robust control for neutral uncertain neural networks with mixed interval time-varying delays,” Nonlinearity, vol. 24, no. 4, pp. 1121–1136, 2011. View at Publisher · View at Google Scholar · View at Scopus
  23. K. Gu, “An integral inequality in the stability problem of time-delay systems,” in Proceedings of the 39th IEEE Confernce on Decision and Control, pp. 2805–2810, December 2000. View at Scopus
  24. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15, SIAM Studies in Applied Mathematics, Philadelphia, Pa, USA, 1994.
  25. G. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge, UK, 1988.
  26. V. B. Kolmanovski and A. D. Myshkis, Applied Theory of Functional Differential Equations, vol. 85, Springer, 1992.
  27. Y. He, M. Wu, G. P. Liu, and J. H. She, “Output feedback stabilization for a discrete-time system with a time-varying delay,” IEEE Transactions on Automatic Control, vol. 53, no. 10, pp. 2372–2377, 2008. View at Publisher · View at Google Scholar · View at Scopus
  28. H. Gao, J. Lam, C. Wang, and Y. Wang, “Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay,” IEE Proceedings Control Theory & Applications, vol. 151, no. 6, pp. 691–698, 2004. View at Google Scholar
  29. L. El Ghaoui, F. Oustry, and M. AitRami, “A cone complementarity linearization algorithm for static output-feedback and related problems,” IEEE Transactions on Automatic Control, vol. 42, no. 8, pp. 1171–1176, 1997. View at Google Scholar · View at Scopus
  30. A. Bellen, N. Guglielmi, and A. E. Ruehli, “Methods for linear systems of circuit delay differential equations of neutral type,” IEEE Transactions on Circuits and Systems I, vol. 46, no. 1, pp. 212–215, 1999. View at Google Scholar · View at Scopus
  31. R. Rakkiyappan, P. Balasubramaniam, and R. Krishnasamy, “Delay-dependent stability of neutral systems with time-varying delays using delay-decomposition approach,” Applied Mathematical Modelling, vol. 36, no. 5, pp. 2253–2261, 2012. View at Publisher · View at Google Scholar
  32. M. N. A. Parlakçi, “Extensively augmented Lyapunov functional approach for the stability of neutral time-delay systems,” IET Control Theory and Applications, vol. 2, no. 5, pp. 431–436, 2008. View at Publisher · View at Google Scholar · View at Scopus
  33. M. N. A. Parlakçi, “Robust stability of uncertain neutral systems: a novel augmented Lyapunov functional approach,” IET Control Theory and Applications, vol. 1, no. 3, pp. 802–809, 2007. View at Publisher · View at Google Scholar · View at Scopus