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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 159279, 12 pages
http://dx.doi.org/10.1155/2013/159279
Research Article

Robust and Passive Constrained Fuzzy Control for Discrete Fuzzy Systems with Multiplicative Noises and Interval Time Delay

1Department of Marine Engineering, National Taiwan Ocean University, Keelung 202, Taiwan
2School of Naval Architecture and Marine Engineering, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, China

Received 18 August 2013; Accepted 1 November 2013

Academic Editor: Baoyong Zhang

Copyright © 2013 Wen-Jer Chang 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. C. Peng and M.-R. Fei, “An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay,” Fuzzy Sets and Systems, vol. 212, no. 2, pp. 97–109, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  2. G. Wei, G. Feng, and Z. Wang, “Robust H control for discrete-time fuzzy systems with infinite-distributed delays,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 1, pp. 224–232, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. Z.-G. Wu, P. Shi, H. Su, and J. Chu, “Reliable H control for discrete-time fuzzy systems with infinite-distributed delay,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 1, pp. 22–31, 2012. View at Publisher · View at Google Scholar · View at Scopus
  4. P. L. Liu, “New results on stability analysis for time-varying delay systems with non-linear perturbations,” ISA Transactions, vol. 52, no. 2, pp. 215–222, 2013. View at Google Scholar
  5. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. Chen, G. Feng, H. Ma, and G. Chen, “Delay-dependent H filter design for discrete-time fuzzy systems with time-varying delays,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 3, pp. 604–616, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. H. Zhang and C. Dang, “Piecewise H controller design of uncertain discrete-time fuzzy systems with time delays,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 6, pp. 1649–1655, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Wu, X. Su, P. Shi, and J. Qiu, “A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 41, no. 1, pp. 273–286, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. B. Zhang and S. Xu, “Delay-Dependent Robust H control for uncertain discrete-time fuzzy systems with time-varying delays,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 4, pp. 809–823, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. H. Gao, X. Liu, and J. Lam, “Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 39, no. 2, pp. 306–317, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. S.-M. Wu, C.-C. Sun, H.-Y. Chung, and W.-J. Chang, “Discrete H2/H nonlinear controller design based on fuzzy region concept and Takagi-Sugeno fuzzy framework,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 53, no. 12, pp. 2838–2848, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  12. P. Vadivel, R. Sakthivel, K. Mathiyalagan, and P. Thangaraj, “Robust stabilisation of non-linear uncertain Takagi-Sugeno fuzzy systems by H control,” IET Control Theory & Applications, vol. 6, no. 16, pp. 2556–2566, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  13. A. H. Besheer, H. M. Emara, and M. M. Abdel Aziz, “Fuzzy-based output-feedback H control for uncertain nonlinear systems: an LMI approach,” IET Control Theory & Applications, vol. 1, no. 4, pp. 1176–1185, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. Dong and G.-H. Yang, “H control for fast sampling discrete-time singularly perturbed systems,” Automatica, vol. 44, no. 5, pp. 1385–1393, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  15. B. Zhang, W. X. Zheng, and S. Xu, “Passivity analysis and passive control of fuzzy systems with time-varying delays,” Fuzzy Sets and Systems, vol. 174, no. 1, pp. 83–98, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. Bemporad, G. Bianchini, and F. Brogi, “Passivity analysis and passification of discrete-time hybrid systems,” IEEE Transactions on Automatic Control, vol. 53, no. 4, pp. 1004–1009, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  17. W.-J. Chang, C.-C. Ku, and P.-H. Huang, “Robust fuzzy control for uncertain stochastic time-delay Takagi-Sugeno fuzzy models for achieving passivity,” Fuzzy Sets and Systems, vol. 161, no. 15, pp. 2012–2032, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. R. Lozano, B. Brogliato, O. Egeland, and B. Maschke, Dissipative Systems Analysis and Control Theory and Applications, Communications and Control Engineering Series, Springer, London, UK, 2000. View at MathSciNet
  19. G. Eli, S. Uri, and Y. Isaac, H Control and Estimation of State-Multiplicative Linear Systems, vol. 318 of Lecture Notes in Control and Information Sciences, Springer, London, UK, 2005. View at MathSciNet
  20. H. Gao, J. Lam, and Z. Wang, “Discrete bilinear stochastic systems with time-varying delay: stability analysis and control synthesis,” Chaos, Solitons & Fractals, vol. 34, no. 2, pp. 394–404, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. S. Xu, J. Lam, and T. Chen, “Robust H control for uncertain discrete stochastic time-delay systems,” Systems & Control Letters, vol. 51, no. 3-4, pp. 203–215, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. Q. Gao, G. Feng, Y. Wang, and J. Qiu, “Universal fuzzy models and universal fuzzy controllers for stochastic nonaffine nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 2, pp. 328–341, 2013. View at Publisher · View at Google Scholar
  23. B. Zhang, S. Xu, G. Zong, and Y. Zou, “Delay-dependent stabilization for stochastic fuzzy systems with time delays,” Fuzzy Sets and Systems, vol. 158, no. 20, pp. 2238–2250, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. H. Huang and D. W. C. Ho, “Delay-dependent robust control of uncertain stochastic fuzzy systems with time-varying delay,” IET Control Theory & Applications, vol. 1, no. 4, pp. 1075–1085, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  25. X. Liu and H. Zhang, “Delay-dependent robust stability of uncertain fuzzy large-scale systems with time-varying delays,” Automatica, vol. 44, no. 1, pp. 193–198, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. C.-C. Ku, P.-H. Huang, and W.-J. Chang, “Observer-based robust fuzzy controller design for uncertain stochastic T-S fuzzy model with passivity performance,” in Proceedings of the 48th IEEE Conference on Decision and Control Held Jointly with the 28th Chinese Control Conference (CDC/CCC '09), pp. 7783–7788, Shanghai, China, December 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. C.-S. Tseng, “Robust fuzzy filter design for a class of nonlinear stochastic systems,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 2, pp. 261–274, 2007. View at Publisher · View at Google Scholar · View at Scopus
  28. X. Su, P. Shi, L. 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 Publisher · View at Google Scholar
  29. Y. Tang, J.-A. Fang, M. Xia, and X. Gu, “Synchronization of Takagi-Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 34, no. 4, pp. 843–855, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. W.-J. Chang, S.-S. Jheng, and C.-C. Ku, “Fuzzy control with robust and passive properties for discrete-time Takagi-Sugeno fuzzy systems with multiplicative noises,” Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering, vol. 226, no. 4, pp. 476–485, 2012. View at Publisher · View at Google Scholar · View at Scopus
  31. W. J. Chang, M. W. Chen, and C. C. Ku, “Passive fuzzy controller design for discrete ship steering systems via Takagi-Sugeno fuzzy model with multiplicative noises,” Journal of Marine Science and Technology, vol. 21, no. 2, pp. 159–165, 2013. View at Google Scholar
  32. Y. Niu and D. W. C. Ho, “Stabilization of discrete-time stochastic systems via sliding mode technique,” Journal of the Franklin Institute, vol. 349, no. 4, pp. 1497–1508, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. X.-L. Zhu and G.-H. Yang, “Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay,” in Proceedings of the American Control Conference (ACC '08), pp. 1644–1649, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  34. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet