H∞ Robust T-S Fuzzy Design for Uncertain Nonlinear Systems with State Delays Based on Sliding Mode Control
Keywords:
sliding mode control, T-S fuzzy model, time-delayed system, H∞ controlAbstract
This paper presents the fuzzy design of sliding mode control (SMC) for nonlinear systems with state delay, which can be represented by a Takagi-Sugeno (TS) model with uncertainties. There exist the parameter uncertainties in both the state and input matrices, as well as the unmatched external disturbance. The key feature of this work is the integration of SMC method with H∞ technique such that the robust asymptotically stability with a prescribed disturbance attenuation level γ can be achieved. A sufficient condition for the existence of the desired SMC is obtained by solving a set of linear matrix inequalities (LMIs). The reachability of the specified switching surface is proven. Simulation results show the validity of the proposed method.References
T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst., Man, Cybern., 15(1):116-132, 1985. http://dx.doi.org/10.1109/TSMC.1985.6313399
Y. Y. Cao, P. M. Frank, Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models, Fuzzy Sets Syst., Vol.124, No.2, pp.213-229, 2001. http://dx.doi.org/10.1016/S0165-0114(00)00120-2
B. Chen, X. P. Liu, S. C. Tong, New delay-dependent stabilization conditions of T-S fuzzy systems with constant delay, Fuzzy Sets Syst., Vol.158, No.20, pp.2209-2224, 2007. http://dx.doi.org/10.1016/j.fss.2007.02.018
E. G. Tian, C. Peng, Delay dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay, Fuzzy Sets Syst., Vol.157, No.4, pp.544-559, 2006. http://dx.doi.org/10.1016/j.fss.2005.06.022
Y. Zhong, Y. P. Yang, New delay-dependent stability analysis and synthesis of T-S fuzzy systems with time-varying delay, Int. J. Robust Nonlinear Control, Vol.20, No.3, pp.313-322, 2009.
P. Chen, Y. C. Tian, Improved delay-dependent robust stabilization conditions of uncertain T-S fuzzy systems with time-varying delay, Fuzzy Sets Syst., Vol.159, No.20, pp.2713-2729, 2008. http://dx.doi.org/10.1016/j.fss.2008.03.009
T. Z. Wu, Design of adaptive variable structure controllers for T-S fuzzy time-delay system, Int. J. Adapt. Control Signal Process., Vol.24, No.2, pp.106-116, 2009. http://dx.doi.org/10.1002/acs.1119
F. Gouaisbaut, M. Dambrine, J. P. Richard, Robust control of delay systems: a sliding mode control design via LMI, Syst. Control Lett., Vol.46, No.4, pp.219-230, 2002. http://dx.doi.org/10.1016/S0167-6911(01)00199-2
W. J. Cao, J. X. Xu, Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems, IEEE Trans. on Autom. Control, Vol.49, No.8, pp.1355-1360, 2004.
H. H. Choi, LMI-Based sliding surface design for integral sliding mode control of mismatched uncertain Systems, IEEE Trans. on Autom. Control, vol.52, no. 4, 736-742, 2007.
B. S. Chen, C. H. Lee, Y. C. Chang, H∞ tracking design of linear systems: Adaptive fuzzy approach, IEEE Trans. Fuzzy Syst., Vol.4, No.1, pp.32-43, 1996. http://dx.doi.org/10.1109/91.481843
Y. He, Q. G. Wang, C. Lin, An improved H∞ filter design for systems with time-varying interval delay, IEEE Trans. Circuits Syst. II: Exp. Briefs, Vol.53, No.11, pp.1235-1239, 2006. http://dx.doi.org/10.1109/TCSII.2006.883209
B. Chen, X. P. Liu, Delay-dependent robust H∞ control for T-S fuzzy systems with time delay, IEEE Trans. Fuzzy Syst., Vol.13, No.26, pp.544-556, 2005. http://dx.doi.org/10.1109/TFUZZ.2004.840112
P. Chen, Y. Dong, Y. C. Tian, New approach on robust delay-dependent H∞ control for uncertain T-S fuzzy systems with interval time-varying delay, IEEE Trans. Fuzzy Syst., Vol.17, No.4, pp.890- 990, 2009. http://dx.doi.org/10.1109/TFUZZ.2008.926586
S. Xu, J. Lam, Robust H∞ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers, IEEE Trans. Fuzzy Syst., Vol.13, No.1, pp.82-93, 2005. http://dx.doi.org/10.1109/TFUZZ.2004.839661
Y.C. Lin, J.C. Lo, Robust mixed H2/H∞ filtering for discrete-time delay fuzzy systems, Int J. Syst. Science, Vol.36, No.15, pp.993-1006, 2005. http://dx.doi.org/10.1080/00207720500404797
P. Gahinet, A. Nemirovski, A. J. Laub and M. Chilali, LMI Control Toolbox, Natick, MA: The MathWorks, 1995.
Published
Issue
Section
License
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.
