Table of Contents Author Guidelines Submit a Manuscript
Journal of Control Science and Engineering
Volume 2015, Article ID 636909, 10 pages
http://dx.doi.org/10.1155/2015/636909
Research Article

Observer Design for a Class of Nonlinear Descriptor Systems: A Takagi-Sugeno Approach with Unmeasurable Premise Variables

1ECPI, Department of Electrical Engineering, ENSEM, University Hassan II of Casablanca, BP 8118, Oasis, 20103 Casablanca, Morocco
2ESPCM, Department of Physics, Faculty of Science, University Ibn Tofail of Kenitra, BP 133, 14 000 Kenitra, Morocco

Received 18 June 2014; Revised 20 January 2015; Accepted 8 March 2015

Academic Editor: Ai-Guo Wu

Copyright © 2015 J. Soulami 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. S. L. Campbell, Singular Systems of Differential Equations, Pitman, London, UK, 1980.
  2. F. L. Lewis, “A survey of linear singular systems,” Circuits, Systems, and Signal Processing, vol. 5, no. 1, pp. 3–36, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. L. Dai, Singular Control Systems, Springer, Berlin, Germany, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  4. 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 Scopus
  5. M. Chadli, D. Maquin, and J. Ragot, “Non quadratic stability analysis of Takagi Sugeno systems,” in Proceedings of the IEEE Conference on Decision and Control (CDC '02), Las Vegas, Nev, USA, 2002.
  6. T. M. Guerra, A. Kruszewski, L. Vermeiren, and H. Tirmant, “Conditions of output stabilization for nonlinear models in the Takagi-Sugeno's form,” Fuzzy Sets and Systems, vol. 157, no. 9, pp. 1248–1259, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. A. Kruszewski, R. Wang, and T. M. Guerra, “Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models: a new approach,” IEEE Transactions on Automatic Control, vol. 53, no. 2, pp. 606–611, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. H. Zhang, Y. Shi, and J. Wang, “On energy-to-peak filtering for nonuniformly sampled nonlinear systems: a markovian jump system approach,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 212–222, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Liu, X. Liu, Y. Shi, and S. Wang, “T-S fuzzy-model-based H2 and H filtering for networked control systems with two-channel Markovian random delays,” Digital Signal Processing, vol. 27, no. 1, pp. 167–174, 2014. View at Publisher · View at Google Scholar · View at Scopus
  10. K. Tanaka and M. Sano, “On the concept of fuzzy regulators and fuzzy observers,” in Proceedings of 3rd IEEE International Conference on Fuzzy Systems, vol. 2, pp. 767–772, June 1994.
  11. K. Tanaka and H. O. Wang, “Fuzzy regulators and fuzzy observers: a linear matrix inequality approach,” in Proceedings of the 36th IEEE Conference on Decision and Control, vol. 2, pp. 1315–1320, San Diego, Calif, USA, December 1997. View at Scopus
  12. K. Tanaka, T. Ikeda, and H. O. Wang, “Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designs,” IEEE Transactions on Fuzzy Systems, vol. 6, no. 2, pp. 250–265, 1998. View at Publisher · View at Google Scholar · View at Scopus
  13. T. A. Johansen, R. Shorten, and R. Murray-Smith, “On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 3, pp. 297–313, 2000. View at Publisher · View at Google Scholar · View at Scopus
  14. P. Bergsten and R. Palm, “Thau-Luenberger observers for TS fuzzy systems,” in Proceedings of the 9th IEEE International Conference on Fuzzy Systems (FUZZ IEEE '00), vol. 2, pp. 671–676, IEEE, San Antonio, Tex, USA, May 2000. View at Scopus
  15. K. Tanaka and H. O. Wan, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley & Sons, 2001.
  16. P. Bergsten, R. Palm, and D. Driankov, “Fuzzy observers,” in Proceedings of the IEEE International Fuzzy Systems Conference, Melbourne, Australia, 2001.
  17. P. Bergsten, R. Palm, and D. Driankov, “Observers for Takagi-Sugeno fuzzy systems,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 32, no. 1, pp. 114–121, 2002. View at Google Scholar
  18. D. Ichalal, B. Marx, J. Ragot, and D. Maquin, “Design of observers for Takagi-Sugeno systems with immeasurable premise variables: an L2 approach,” in Proceedings of the 17th World Congress, International Federation of Automatic Control (IFAC '08), Seoul, Korea, July 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. D. Ichalal, B. Marx, J. Ragot, and D. Maquin, “State and unknown input estimation for nonlinear systems described by Takagi-Sugeno models with unmeasurable premise variables,” in Proceedings of the 17th Mediterranean Conference on Control and Automation (MED '09), pp. 217–222, Thessaloniki, Greece, June 2009. View at Publisher · View at Google Scholar
  20. A. M. Nagy, G. Mourot, B. Marx, G. Schutz, and J. Ragot, “Model structure simplification of a biological reactor,” in Proceedings of the 15th IFAC Symposium on System Identification (SYSID '09), pp. 257–262, Saint-Malo, France, July 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. T. Taniguchi, K. Tanaka, and H. O. Wang, “Fuzzy descriptor systems and nonlinear model following control,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 4, pp. 442–452, 2000. View at Publisher · View at Google Scholar · View at Scopus
  22. C. Lin, Q.-G. Wang, and T. H. Lee, “Stability and stabilization of a class of fuzzy time-delay descriptor systems,” IEEE Transactions on Fuzzy Systems, vol. 14, no. 4, pp. 542–551, 2006. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Essabre, J. Soulami, and E. Elyaagoubi, “Design of state observer for a class of non linear singular systems described by Takagi-Sugeno model,” Contemporary Engineering Sciences, vol. 6, no. 1–4, pp. 99–109, 2013. View at Google Scholar · View at Scopus
  24. H. Hamdi, M. Rodrigues, C. Mechmech, and N. Benhadj Braiek, “Observer based fault tolerant control for Takagi-Sugeno nonlinear descriptor systems,” in Proceedings of the International Conference on Control, Engineering & Information Technology (CEIT '13), vol. 1, pp. 52–57, 2013.
  25. M. Essabre, J. Soulami, A. El Assoudi, E. H. El Yaagoubi, and E. M. El Bouatmani, “Fuzzy observer design for a class of takagi-sugeno descriptor systems,” Contemporary Engineering Sciences, vol. 7, no. 1–4, pp. 149–164, 2014. View at Publisher · View at Google Scholar · View at Scopus
  26. T. Taniguchi, K. Tanaka, H. Ohtake, and H. O. Wang, “Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 9, no. 4, pp. 525–538, 2001. View at Publisher · View at Google Scholar · View at Scopus