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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 916357, 11 pages
http://dx.doi.org/10.1155/2013/916357
Research Article

BIBO Stabilization of Discrete-Time Stochastic Control Systems with Mixed Delays and Nonlinear Perturbations

1School of Mathematics and Computational Science, Fuyang Teachers College, Fuyang 236037, China
2Department of Mathematics, Anhui Normal University, Wuhu 241000, China
3College of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China

Received 19 March 2013; Revised 23 May 2013; Accepted 6 June 2013

Academic Editor: Sakthivel Rathinasamy

Copyright © 2013 Xia Zhou 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. R. Sakthivel, K. Mathiyalagan, and S. M. Anthoni, “Robust stability and control for uncertain neutral time delay systems,” International Journal of Control, vol. 85, no. 4, pp. 373–383, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Lakshmanan, J. H. Park, D. H. Ji, H. Y. Jung, and G. Nagamani, “State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory,” Nonlinear Dynamics, vol. 70, no. 2, pp. 1421–1434, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  3. R. Sakthivel, K. Mathiyalagan, and S. Marshal Anthoni, “Robust H control for uncertain discrete-time stochastic neural networks with time-varying delays,” IET Control Theory & Applications, vol. 6, no. 9, pp. 1220–1228, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  4. P. Balasubramaniam, S. Lakshmanan, and A. Manivannan, “Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays,” Chaos, Solitons and Fractals, vol. 45, no. 4, pp. 483–495, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. K. Mathiyalagan, R. Sakthivel, and S. Marshal Anthoni, “Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks,” Physics Letters A, vol. 376, no. 8-9, pp. 901–912, 2012. View at Publisher · View at Google Scholar · View at Scopus
  6. A. Arunkumar, R. Sakthivel, K. Mathiyalagan, and S. Marshal Anthoni, “Robust stability criteria for discrete-time switched neural networks with various activation functions,” Applied Mathematics and Computation, vol. 218, no. 22, pp. 10803–10816, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  7. S. Lakshmanan and P. Balasubramaniam, “New results of robust stability analysis for neutral-type neural networks with time-varying delays and Markovian jumping parameters,” Canadian Journal of Physics, vol. 89, no. 8, pp. 827–840, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. P. Vadivel, R. Sakthivel, K. Mathiyalagan, and P. Thangaraj, “Robust stabilization of nonlinear uncertain Takagi-Sugeno fuzzy systems by H control,” IET Control Theory and Applications, vol. 6, pp. 2556–2566, 2012.
  9. Z. Liu, S. Lü, S. Zhong, and M. Ye, “Improved robust stability criteria of uncertain neutral systems with mixed delays,” Abstract and Applied Analysis, Article ID 294845, 18 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. F. Qiu, B. Cui, and Y. Ji, “Delay-dividing approach for absolute stability of Lurie control system with mixed delays,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 3110–3120, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. X. Wang, Q. Guo, and D. Xu, “Exponential p-stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,” Mathematics and Computers in Simulation, vol. 79, no. 5, pp. 1698–1710, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  12. W. Zhou, H. Lu, and C. Duan, “Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity,” Neurocomputing, vol. 72, no. 13–15, pp. 3357–3365, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Zhang, S. Xu, and Z. Zeng, “Novel robust stability criteria of discrete-time stochastic recurrent neural networks with time delay,” Neurocomputing, vol. 72, no. 13–15, pp. 3343–3351, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. C. Peng and Y.-C. Tian, “Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay,” Journal of Computational and Applied Mathematics, vol. 214, no. 2, pp. 480–494, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Z. Wu, H. Su, J. Chu, and W. Zhou, “Improved result on stability analysis of discrete stochastic neural networks with time delay,” Physics Letters A, vol. 373, no. 17, pp. 1546–1552, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. R. Sakthivel, S. Santra, and K. Mathiyalagan, “Admissibility analysis and control synthesis for descriptor systems with random abrupt changes,” Applied Mathematics and Computation, vol. 219, no. 18, pp. 9717–9730, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Y. Liu, Z. Wang, and X. Liu, “State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays,” Physics Letters A, vol. 372, no. 48, pp. 7147–7155, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Y. Tang, J.-A. Fang, M. Xia, and D. Yu, “Delay-distribution-dependent stability of stochastic discrete-time neural networks with randomly mixed time-varying delays,” Neurocomputing, vol. 72, no. 16–18, pp. 3830–3838, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. Y. Liu, Z. Wang, and X. Liu, “Asymptotic stability for neural networks with mixed time-delays: the discrete-time case,” Neural Networks, vol. 22, no. 1, pp. 67–74, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. P. Li and S.-m. Zhong, “BIBO stabilization for system with multiple mixed delays and nonlinear perturbations,” Applied Mathematics and Computation, vol. 196, no. 1, pp. 207–213, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. T. Bose and M. Q. Chen, “BIBO stability of the discrete bilinear system,” Digital Signal Processing, vol. 5, no. 3, pp. 160–166, 1995. View at Publisher · View at Google Scholar · View at Scopus
  22. S. M. Zhong and Y. Q. H. Uang, “BIBO stabilization of nonlinear system with time-delay,” Journal of University of Electronic Science and Technology of China, vol. 32, no. 4, pp. 655–657, 2000.
  23. K. C. Cao, S. M. Zhong, and B. S. Liu, “BIBO and robust stabilization for system with time-delay and nonlinear perturbations,” Journal of University of Electronic Science and Technology of China, vol. 32, no. 6, pp. 787–789, 2003.
  24. J. R. Partington and C. Bonnet, “H and BIBO stabilization of delay systems of neutral type,” Systems & Control Letters, vol. 52, no. 3-4, pp. 283–288, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. A. T. Tomerlin and W. W. Edmonson, “BIBO stability of d-dimensional filters,” Multidimensional Systems and Signal Processing, vol. 13, no. 3, pp. 333–340, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  26. Y. Q. Huang, W. Zeng, and S. M. Zhong, “BIBO stabukuty of continuous time systems,” Journal of University of Electronic Science and Technology of China, vol. 3, no. 2, pp. 178–181, 2005.
  27. P. Li and S.-m. Zhong, “BIBO stabilization of time-delayed system with nonlinear perturbation,” Applied Mathematics and Computation, vol. 195, no. 1, pp. 264–269, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. Z. X. Liu, S. Lv, and S. M. Zhong, “Augmented Lyapunov method for BIBO stabilization of discrete system,” Journal of Mathematics Research, vol. 2, pp. 116–122, 2011.
  29. P. Li and S.-M. Zhong, “BIBO stabilization of piecewise switched linear systems with delays and nonlinear perturbations,” Applied Mathematics and Computation, vol. 213, no. 2, pp. 405–410, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. P. Li, S.-m. Zhong, and J.-z. Cui, “Delay-dependent robust BIBO stabilization of uncertain system via LMI approach,” Chaos, Solitons and Fractals, vol. 40, no. 2, pp. 1021–1028, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. Y. Fu and X. Liao, “BIBO stabilization of stochastic delay systems with uncertainty,” Institute of Electrical and Electronics Engineers, vol. 48, no. 1, pp. 133–138, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  32. X. Zhou and S. Zhong, “Riccati equations and delay-dependent BIBO stabilization of stochastic systems with mixed delays and nonlinear perturbations,” Advances in Difference Equations, Article ID 494607, 14 pages, 2010. View at Zentralblatt MATH · View at MathSciNet
  33. D. Yue, “Robust stabilization of uncertain systems with unknown input delay,” Automatica, vol. 40, no. 2, pp. 331–336, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet