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Abstract and Applied Analysis
Volume 2013, Article ID 151374, 8 pages
http://dx.doi.org/10.1155/2013/151374
Research Article

State-Feedback Stabilization for a Class of Stochastic Feedforward Nonlinear Time-Delay Systems

1College of Engineering, Bohai University, Liaoning 121013, China
2College of Information Science, Bohai University, Liaoning 121013, China
3Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway

Received 18 October 2013; Accepted 18 November 2013

Academic Editor: Ming Liu

Copyright © 2013 Liang 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. N. Duan and X.-J. Xie, “Further results on output-feedback stabilization for a class of stochastic nonlinear systems,” IEEE Transactions on Automatic Control, vol. 56, no. 5, pp. 1208–1213, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. Krstić and H. Deng, Stabilization of Uncertain Nonlinear Systems, Springer, New York, NY, USA, 1998.
  3. S. Kuang, Y. Peng, F. Deng, and W. Gao, “Exponential stability and numerical methods of stochastic recurrent neural networks with delays,” Abstract and Applied Analysis, vol. 2013, Article ID 761237, 11 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  4. W.-Q. Li and X.-J. Xie, “Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable,” Automatica, vol. 45, no. 2, pp. 498–503, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. L. Liu and X.-J. Xie, “Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay,” Automatica, vol. 47, no. 12, pp. 2772–2779, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S.-J. Liu, S. S. Ge, and J.-F. Zhang, “Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays,” International Journal of Control, vol. 81, no. 8, pp. 1210–1220, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S.-J. Liu, J.-F. Zhang, and Z.-P. Jiang, “Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems,” Automatica, vol. 43, no. 2, pp. 238–251, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Y.-G. Liu and J.-F. Zhang, “Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zero-dynamics,” SIAM Journal on Control and Optimization, vol. 45, no. 3, pp. 885–926, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. L. Wu, P. Shi, and H. Gao, “State estimation and sliding-mode control of Markovian jump singular systems,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1213–1219, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  10. Z.-J. Wu, X.-J. Xie, and S.-Y. Zhang, “Adaptive backstepping controller design using stochastic small-gain theorem,” Automatica, vol. 43, no. 4, pp. 608–620, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Z.-J. Wu, X.-J. Xie, P. Shi, and Y.-Q. Xia, “Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching,” Automatica, vol. 45, no. 4, pp. 997–1004, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. X.-J. Xie and N. Duan, “Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1197–1202, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  13. X.-J. Xie and L. Liu, “Further results on output feedback stabilization for stochastic high-order nonlinear systems with time-varying delay,” Automatica, vol. 48, no. 10, pp. 2577–2586, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. X.-J. Xie and L. Liu, “A homogeneous domination approach to state feedback of stochastic high-order nonlinear systems with time-varying delay,” IEEE Transactions on Automatic Control, vol. 58, no. 2, pp. 494–499, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. X.-J. Xie and J. Tian, “Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization,” Automatica, vol. 45, no. 1, pp. 126–133, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. Yin, S. X. Ding, A. H. A. Sari, and H. Hao, “Data-driven monitoring for stochastic systems and its application on batch process,” International Journal of Systems Science, vol. 44, no. 7, pp. 1366–1376, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  17. X. Yu and X.-J. Xie, “Output feedback regulation of stochastic nonlinear systems with stochastic iISS inverse dynamics,” IEEE Transactions on Automatic Control, vol. 55, no. 2, pp. 304–320, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  18. X. Zhao, M. Ling, and Q. Zeng, “Delay-dependent robust control for uncertain stochastic systems with Markovian switching and multiple delays,” Journal of Systems Engineering and Electronics, vol. 21, no. 2, pp. 287–295, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. X. Zhou, Y. Ren, and S. Zhong, “BIBO stabilization of discrete-time stochastic control systems with mixed delays and nonlinear perturbations,” Abstract and Applied Analysis, vol. 2013, Article ID 916357, 11 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  20. F. Mazenc and S. Bowong, “Tracking trajectories of the cart-pendulum system,” Automatica, vol. 39, no. 4, pp. 677–684, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. R. Sepulchre, M. Janković, and P. V. Kokotović, Constructive Nonlinear Control, Springer, London, UK, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  22. N. Bekiaris-Liberis and M. Krstić, “Delay-adaptive feedback for linear feedforward systems,” Systems & Control Letters, vol. 59, no. 5, pp. 277–283, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. S. Ding, C. Qian, S. Li, and Q. Li, “Global stabilization of a class of upper-triangular systems with unbounded or uncontrollable linearizations,” International Journal of Robust and Nonlinear Control, vol. 21, no. 3, pp. 271–294, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. A. Isidori, Nonlinear Control Systems, Springer, London, UK, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  25. M. Krstić, “Input delay compensation for forward complete and strict-feedforward nonlinear systems,” IEEE Transactions on Automatic Control, vol. 55, no. 2, pp. 287–302, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  26. C. Qian and J. Li, “Global output feedback stabilization of upper-triangular nonlinear systems using a homogeneous domination approach,” International Journal of Robust and Nonlinear Control, vol. 16, no. 9, pp. 441–463, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. X. Ye, “Adaptive stabilization of time-delay feedforward nonlinear systems,” Automatica, vol. 47, no. 5, pp. 950–955, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. X. Zhang, L. Baron, Q. Liu, and E.-K. Boukas, “Design of stabilizing controllers with a dynamic gain for feedforward nonlinear time-delay systems,” IEEE Transactions on Automatic Control, vol. 56, no. 3, pp. 692–697, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  29. X. Zhang, Q. Liu, L. Baron, and E.-K. Boukas, “Feedback stabilization for high order feedforward nonlinear time-delay systems,” Automatica, vol. 47, no. 5, pp. 962–967, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. L. Liu and X.-J. Xie, “State feedback stabilization for stochastic feedforward nonlinear systems with time-varying delay,” Automatica, vol. 49, no. 4, pp. 936–942, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  31. H. K. Khalil, Nonlinear Systems, Prentice-Hall, Upper Saddle River, NJ, USA, 3rd edition, 2002.
  32. L. Zhang and H. Gao, “Asynchronously switched control of switched linear systems with average dwell time,” Automatica, vol. 46, no. 5, pp. 953–958, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. H. L. Dong, Z. D. Wang, and H. J. Gao, “Distributed H filtering for a class of markovian jump nonlinear time-delay systems over lossy sensor networks,” IEEE Transactions on Industrial Electronics, vol. 60, no. 10, pp. 4665–4672, 2013. View at Google Scholar
  34. X. C. Xie, S. Yin, H. J. Gao, and O. Kaynak, “Asymptotic stability and stabilisation of uncertain delta operator systems with time-varying delays,” IET Control Theory and Applications, vol. 7, no. 8, pp. 1071–1078, 2013. View at Google Scholar
  35. S. Yin, S. X. Ding, and H. Luo, “Real-time implementation of fault tolerant control system with performance optimization,” IEEE Transactions on Industrial Electronics, vol. 61, no. 5, pp. 2402–2411, 2014. View at Google Scholar
  36. H. Gao and T. Chen, “H estimation for uncertain systems with limited communication capacity,” IEEE Transactions on Automatic Control, vol. 52, no. 11, pp. 2070–2084, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  37. H. Gao, T. Chen, and J. Lam, “A new delay system approach to network-based control,” Automatica, vol. 44, no. 1, pp. 39–52, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. H. Gao and T. Chen, “Network-based H output tracking control,” IEEE Transactions on Automatic Control, vol. 53, no. 3, pp. 655–667, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  39. H. Gao, X. Meng, and T. Chen, “Stabilization of networked control systems with a new delay characterization,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2142–2148, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  40. H. Li, H. Gao, and P. Shi, “New passivity analysis for neural networks with discrete and distributed delays,” IEEE Transactions on Neural Networks, vol. 21, no. 11, pp. 1842–1847, 2010. View at Publisher · View at Google Scholar · View at Scopus
  41. J. Qiu, G. Feng, and H. Gao, “Fuzzy-model-based piecewise H static-output-feedback controller design for networked nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 5, pp. 919–934, 2010. View at Publisher · View at Google Scholar · View at Scopus