Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 235804, 11 pages
http://dx.doi.org/10.1155/2014/235804
Research Article

Robust Fuzzy Control for Nonlinear Discrete-Time Stochastic Systems with Markovian Jump and Parametric Uncertainties

College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China

Received 4 May 2014; Revised 2 August 2014; Accepted 3 August 2014; Published 18 August 2014

Academic Editor: Peng Shi

Copyright © 2014 Huiying Sun and Long Yan. 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. S. Saat, D. Huang, and S. K. Nguang, “Robust state feedback control of uncertain polynomial discrete-time systems: an integral action approach,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 3, pp. 1233–1244, 2013. View at Google Scholar · View at Scopus
  2. R. N. Yang, P. Shi, G. P. Liu, and H. J. Gao, “Network-based feedback control for systems with mixed delays based on quantization and dropout compensation,” Automatica, vol. 47, no. 12, pp. 2805–2809, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. J. H. Zhang, M. F. Ren, Y. Tian, G. L. Hou, and F. Fang, “Constrained stochastic distribution control for nonlinear stochastic systems with non-Gaussian noises,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 4, pp. 1759–1767, 2013. View at Google Scholar · View at Scopus
  4. R. Yang, P. Shi, and G. Liu, “Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts,” IEEE Transactions on Automatic Control, vol. 56, no. 11, pp. 2655–2660, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. S. G. Cao, N. W. Rees, and G. Feng, “H control of uncertain dynamical fuzzy discrete-time systems,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 31, no. 5, pp. 802–812, 2001. View at Publisher · View at Google Scholar · View at Scopus
  6. X. J. Su, P. Shi, L. G. Wu, and S. K. Nguang, “Induced l2 filtering of fuzzy stochastic systems with time-varying delays,” IEEE Transactions on Cybernetics, vol. 43, no. 4, pp. 1251–1264, 2013. View at Google Scholar
  7. Y. Y. Cao and P. M. Frank, “Robust H disturbance attenuation for a class of uncertain discrete-time fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 4, pp. 406–415, 2000. View at Publisher · View at Google Scholar · View at Scopus
  8. D. J. Choi and P. Park, “H∞ state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting-dependent lyapunov functions,” IEEE Transactions on Fuzzy Systems, vol. 11, no. 2, pp. 271–278, 2003. View at Publisher · View at Google Scholar · View at Scopus
  9. G. Feng, “Stability analysis of piecewise discrete-time linear systems,” IEEE Transactions on Automatic Control, vol. 47, no. 7, pp. 1108–1112, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. G. Feng and J. Ma, “Quadratic stabilization of uncertain discrete-time fuzzy dynamic systems,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 48, no. 11, pp. 1337–1343, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. R. Qi, L. Zhu, and B. Jiang, “Fault-tolerant reconfigurable control for MIMO systems using online fuzzy identification,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 10, pp. 3915–3928, 2013. View at Google Scholar · View at Scopus
  12. X. J. Su, L. G. Wu, and P. Shi, “Sensor networks with random link failures: distributed filtering for T-S fuzzy systems,” IEEE Transactions on Industrial Informatics, vol. 9, no. 3, pp. 1739–1750, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. Z. Lin, Y. Lin, and W. H. Zhang, “H stabilisation of non-linear stochastic active fault-tolerant control systems: fuzzy-interpolation approach,” IET Control Theory &; Applications, vol. 4, no. 10, pp. 2003–2017, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. S. Zhou, G. Feng, J. Lam, and S. Xu, “Robust H control for discrete-time fuzzy systems via basis-dependent Lyapunov functions,” Information Sciences, vol. 174, no. 3-4, pp. 197–217, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. Mariton, Jump Linear Systems in Automatic Control, Marcel Dekker, New York, NY, USA, 1990.
  16. Y. D. Ji and H. J. Chizeck, “Controllability, observability and discrete-time Markovian jump linear quadratic control,” International Journal of Control, vol. 48, no. 2, pp. 481–498, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. O. L. V. Costa and M. D. Fragoso, “Stability results for discrete-time linear systems with Markovian jumping parameters,” Journal of Mathematical Analysis and Applications, vol. 179, no. 1, pp. 154–178, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. W. H. Zhang and B. S. Chen, “On stabilizability and exact observability of stochastic systems with their applications,” Automatica, vol. 40, no. 1, pp. 87–94, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. Y. G. Fang and K. A. Loparo, “Stabilization of continuous-time jump linear systems,” IEEE Transactions on Automatic Control, vol. 47, no. 10, pp. 1590–1603, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. X. Feng, K. A. Loparo, Y. Ji, and H. J. Chizeck, “Stochastic stability properties of jump linear systems,” IEEE Transactions on Automatic Control, vol. 37, no. 1, pp. 38–53, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. L. Arnold, W. Kliemann, and E. Oelijeklaus, “Lyapunov exponents of linear stochastic systems,” in Lyapunov Exponents, vol. 1186 of Lecture Notes in Mathematics, pp. 85–125, Springer, Berlin, Germany, 1986. View at Google Scholar
  22. O. L. V. Costa, J. B. R. do Val, and J. C. Geromel, “A convex programming approach to H2-control of discrete-time Markovian jump linear systems,” International Journal of Control, vol. 66, no. 4, pp. 557–580, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. H. Sun, L. Jiang, and W. Zhang, “Feedback control on nash equilibrium for discrete-time stochastic systems with markovian jumps: finite-horizon case,” International Journal of Control, Automation and Systems, vol. 10, no. 5, pp. 940–946, 2012. View at Publisher · View at Google Scholar · View at Scopus
  24. O. L. V. Costa and R. P. Marques, “Mixed H2/Hcontrol of discrete-time Markovian jump linear systems,” IEEE Transactions on Automatic Control, vol. 43, no. 1, pp. 95–100, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. D. Hinrichsen and A. J. Pritchard, “Stochastic H,” SIAM Journal on Control and Optimization, vol. 36, no. 5, pp. 1504–1538, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. W. Zhang and B. Chen, “State feedback H control for a class of nonlinear stochastic systems,” SIAM Journal on Control and Optimization, vol. 44, no. 6, pp. 1973–1991, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. E. Boukas and P. Shi, “Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters,” International Journal of Robust and Nonlinear Control, vol. 8, no. 13, pp. 1155–1167, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  28. T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man and Cybernetics, vol. 15, no. 1, pp. 116–132, 1985. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  29. H. J. Lee, J. B. Park, and G. Chen, “Robust fuzzy control of nonlinear systems with parametric uncertainties,” IEEE Transactions on Fuzzy Systems, vol. 9, no. 2, pp. 369–379, 2001. View at Publisher · View at Google Scholar · View at Scopus
  30. K. Tanaka and M. Sano, “Robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer,” IEEE Transactions on Fuzzy Systems, vol. 2, no. 2, pp. 119–134, 1994. View at Publisher · View at Google Scholar · View at Scopus