Skip to main content
SpringerLink
Log in

Robust H ∞ static output feedback stabilization of T-S fuzzy systems subject to actuator saturation

  • Regular Papers
  • Intelligent and Information Systems
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper proposes a method for designing robust H∞ static output feedback stabilization of Takagi-Sugeno (T-S) fuzzy systems under actuator saturation. In this paper, the input saturation is represented by a polytopic model and the modeling error is assumed a norm-bounded uncertainty. A set invariance condition for robust H∞ static output feedback system under actuator saturation is first established. Then, the estimation of the largest domain of attraction for the system is formulated and solved as a Linear Matrix Inequality (LMI) optimization problem. Two examples are used to demonstrate the effectiveness of the proposed design method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Takagi and M. Sugeno, “Fuzzy identification of systems and its application to modeling and control,” IEEE Trans. on Systems, Man, Cybernetics, vol. 15, pp. 116–132, 1985.

    MATH  Google Scholar 

  2. H. O. Wong, K. Tanaka, and M. F. Griffin, “An approach to fuzzy control of nonlinear systems: stability and design,” IEEE Trans. on Fuzzy System, vol. 4, no. 1, pp. 14–23, 1996.

    Article  Google Scholar 

  3. Y. Y. Cao and Z. Lin, “Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation,” IEEE Trans. on systems, vol. 11, no. 1, pp. 57–67, 2003.

    Article  Google Scholar 

  4. 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 & Systems, vol. 157, no. 9, May 2006.

  5. C. H. Fang, Y. S. Liu, S. W. Kau, L. Hong, and C. H. Lee, “A new LMI-Based approach to relaxed quadratic stabilization of T-S fuzzy control systems,” IEEE Trans. on Fuzzy Systems, vol. 14, no. 3, pp. 386–397, 2006.

    Article  Google Scholar 

  6. J. Li, S. Zhou, and S. Xu, “Fuzzy control design via fuzzy Lyapunov functions,” IEEE Trans. on Systems, vol. 38, no. 6, pp. 1657–1661, 2008.

    Google Scholar 

  7. M. Chadli, “On the stability analysis of uncertain fuzzy models,” International Journal of Fuzzy Systems, vol. 8, no. 4, pp. 224–231, 2006.

    MathSciNet  Google Scholar 

  8. S. H. Kim and P. G. Park, “H∞ state-feedback control design for fuzzy systems using Lyapunov function with quadratic dependence on fuzzy weighting function,” IEEE Trans. on Fuzzy System, vol. 16, pp. 1655–1663, 2008.

    Article  Google Scholar 

  9. M. Chadli, A. Akhenak, J. Ragot, and D. Maquin, “State and unknown input estimation for discrete time multiple model,” Journal of the Franklin Institute, vol. 346, no. 6, pp. 593–610, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  10. T. Zhang, G. Feng, H. Liu, and J. Lu, “Piecewise fuzzy Anti-Windup dynamic output feedback control of nonlinear processes with amplitude and rate actuator saturations,” IEEE Trans. on Fuzzy System, vol. 17, no. 2, pp. 253–263, 2009.

    Article  Google Scholar 

  11. Q. Zheng and F. Wu, “Output feedback control of saturated discrete-time linear systems using parameter dependent Lyapunov functions,” System & Control Letters, vol. 57, no. 11, pp. 896–903, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. C. Lo and M. L. Lin, “Robust H∞ nonlinear control via fuzzy static output feedback,” IEEE on Trans. on Circuits and Systems I, vol. 50, no. 11, pp. 1494–1502, 2003.

    Article  MathSciNet  Google Scholar 

  13. M. Chadli, D. Maquin, and J. Ragot, “Static output feedback for Takagi-Sugeno systems: an LMI approach,” Proc. of the 10th Mediterranean Conference on Control and Automation, 2002.

  14. M. Chadli and T.-M. Guerra. “LMI solution for robust static output feedback control of Takagi-Sugeno fuzzy models,” IEEE Trans. on Fuzzy Systems. In press, 2012.

  15. H. N. Wu, “Robust H2 fuzzy output feedback control for discrete-time nonlinear systems with parametric uncertainties,” International Journal of Approximate Reasoning, vol. 46, no. 1, pp. 151–165, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Dong and G. H. Yang, “Static output feedback control of a class of nonlinear discrete-time systems,” Fuzzy Sets and Systems, vol. 160, no. 19, pp. 2844–2859, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  17. H. J. Lee and D. W. Kim, “Robust stabilization of T-S fuzzy systems: fuzzy static output feedback under parametric uncertainty,” International Journal of Control, Automation and Systems, vol. 7, no. 5, pp. 731–736, 2009.

    Article  Google Scholar 

  18. Jr. Jomas da Silva and S. Tarbouriech, “Antiwindup design region of stability for discrete-time linear systems,” System & Control Letters, vol. 55, pp. 184–192, 2006.

    Article  Google Scholar 

  19. D. Henrion and S. Tarbouriech, “LMI relaxations for robust stability of linear systems with saturating,” Automatica, vol. 35, no. 9, pp. 1599–1604, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  20. A. Benzaouia, O. Benmessaouda, and F. Tadeo, “Stabilization of uncertain saturated discrete-time switching systems,” International Journal of Control, Automation and Systems, vol. 7, no. 5, pp. 835–841, 2009.

    Article  Google Scholar 

  21. H. Han, “T-S fuzzy controller in consideration of input constraint,” Proc. of the 2nd International Conference on Innovative Computing, Information and Control, 5–7 September, Kumamoto, Japan 2007.

  22. S. H. Kim, C. H. Lee, and P. G. Park, “H∞ statefeedback control for fuzzy systems with input saturation via fuzzy weighting-dependent Lyapunov functions,” Computers and Mathematics with Applications, vol. 57, no. 6, pp. 981–990, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  23. N. Kapoor and P. Daoutidis, “Stabilization of non linear processes with input constraints,” Computers and Chemical Engineering, vol. 24, no. 1, pp. 9–21, 2000.

    Article  Google Scholar 

  24. T. Hu, A. R. Teel, and L. Zaccarian, “Anti-windup synthesis for linear control systems with input saturation,” Automatica, vol. 44, no. 2, pp. 512–519, 2008.

    Article  MathSciNet  Google Scholar 

  25. S. Tarbouriech and J. M. Biannic, “Optimisation and implementation of dynamic anti-windup compensator with multiple saturation in flight control system,” Control Engineering Practice, vol. 17, no. 6, pp. 703–713, 2009.

    Article  Google Scholar 

  26. D. Dai, T. Hu, A. R. Teel, and L. Zaccarian, “Piecewise quadratic Lyapunov functions for system with dead zones or saturations,” System & Control Letters, vol. 58, no. 5, pp. 365–371, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  27. H. Ohtake, K. Tanaka, and H. Wang, “Fuzzy model-based servo control for nonlinear systems with Input constraint,” Proc. of IEEE International Symposium on Intelligent Control, pp. 452–455, 2009.

  28. H. Du and N. Zhang, “Fuzzy control for nonlinear uncertain electrohydraulic active suspensions with input constraint,” IEEE Trans. on Fuzzy System, vol. 17, no. 2, pp. 343–356, 2009.

    Article  Google Scholar 

  29. J. G. Chase, S. E. Breneman, and H. A. Smith, “Robust H-infinity static output feedback control with actuator saturation,” Journal of Engineering Mechanics, vol. 125, no. 2, pp. 225–233, 1999.

    Article  Google Scholar 

  30. J. C. Lo and M. L. Lin, “Robust H∞ nonlinear control via fuzzy static output feedback,” IEEE on Trans. on Circuits and Systems I, vol. 50, no. 11, pp. 1494–1502, 2003.

    Article  MathSciNet  Google Scholar 

  31. H. Yoneyama, “Robust stability and stabilization for uncertain Takagi-Sugeno fuzzy time-delay systems,” Fuzzy Sets and Systems, vol. 55, pp. 115–134, 2007.

    Article  MathSciNet  Google Scholar 

  32. M. Bouattour, M. Chadli, M. Chaabane, and A. El Hajjaji, “Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach,” International Journal of Control, Automation and Systems, vol. 9, no. 5, pp. 973–979, Oct. 2011.

    Article  Google Scholar 

  33. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994.

    Book  MATH  Google Scholar 

  34. L. Xiaodong and Z. Qingling, “New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI,” Automatica, vol. 39, no. 9, pp. 1571–1582, 2003.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science and Technology, University of Jijel LAMEL, BP. 98, Ouled Aissa, Jijel, 18000, Algeria

    Dounia Saifia & Salim Labiod

  2. MIS (EA 4290), University of Picardie Jules Verne, 7, Rue du Moulin Neuf, 80000, Amiens, France

    Mohammed Chadli

  3. LAMIH, UMR CNRS 8530, Université de Valenciennes et du Hainaut-Cambrésis, Le Mont-Houy, 59313, Valenciennes cedex 9, France

    Thierry Marie Guerra

Authors
  1. Dounia Saifia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammed Chadli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Salim Labiod
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thierry Marie Guerra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammed Chadli.

Additional information

Recommended by Editorial Board member Euntai Kim under the direction of Editor Young-Hoon Joo.

Dounia Saifia is currently an assistant professor at the University of Jijel, Algeria. She received her Eng. degree in 2001 and Magister degree in 2004, in automatic control from the University of Annaba, Algeria. She is currently a Ph.D. candidate in automatic control at the University of Jijel. Her research interests include nonlinear control, actuator saturations and multiple model.

Mohammed Chadli received his Master degree (DEA) from INSA of Lyon, France in 1999, the Ph.D. thesis from CRAN-INPL of Nancy in 2002 and the HDR in 2011. Since 2004, he has been an Assoc. Professor (Maitre de Conférences) at the University of Picardie Jules Verne, Laboratory of’ Modélisation, Information et Systèmes’ in Amiens. He is a senior member of the IEEE and associate editor in international journals. His research interests include, on the theoretical side, analysis and control of singular systems, switched/LPV/fuzzy Takagi-Sugeno models, model-based diagnosis (FDI), fault tolerant control (FTC), analysis/control via LMI optimization and Lyapunov methods. On the application side he is mainly interested in automotive control.

Salim Labiod is currently an Associate Professor at the University of Jijel, Algeria. He received his Ph.D. degree in control engineering from the National Polytechnic School of Algiers in 2005 and his Habilitation in 2007. His research interests include fuzzy control, adaptive control, and nonlinear control.

Thierry Marie Guerra was born in Mulhouse, France in 1963. He is currently a professor at the University of Valenciennes et du Hainaut-Cambrésis (UVHC), France. He received his Ph.D. degree in automatic control from the UVHC in 1991 and the HDR in 1999. He is head of the Laboratory of Industrial and Human Automation, Mechanics and Computer Science (LAMIH CNRS UMR 8201) (95 researchers and staff, 75 Ph.D. students and post-docs). He is vice-chair of the Technical Committee 3.2 “Computational Intelligence in Control” for IFAC (International Federation of Automatic Control), member of the IFAC TC 7.1 “Automotive Control”, Area Editor of the international journal Fuzzy Sets & Systems and of IEEE Transactions on Vehicular Technology. His major research fields and topics of interest are nonlinear control, LPV, quasi-LPV (Takagi-Sugeno) models control and observation, LMI constraints, Non quadratic Lyapunov functions. Applications to powertrain systems (IC engine, electrical motors, hybrid vehicles, fuel cells ...).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saifia, D., Chadli, M., Labiod, S. et al. Robust H ∞ static output feedback stabilization of T-S fuzzy systems subject to actuator saturation. Int. J. Control Autom. Syst. 10, 613–622 (2012). https://doi.org/10.1007/s12555-012-0319-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-012-0319-3

Keywords

Search

Navigation