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Stabilization of a certain class of fuzzy control systems with uncertainties

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we investigate the global uniform practical exponential stability for a class of uncertain Takagi-Sugeno fuzzy systems. The uncertainties are supposed uniformly to be bounded by some known integrable functions to obtain an exponential convergence toward a neighborhood of the origin. Therefore, we use common quadratic Lyapunov function (CQLF) and parallel distributed compensation (PDC) controller techniques to show the global uniform practical exponential stability of the closed-loop system. Numeric simulations are given to validate the proposed approach.
Rocznik
Strony
453--481
Opis fizyczny
Bibliogr. 33 poz., wykr., wzory
Twórcy
autor
  • University of Sfax, Tunisia, Faculty of Sciences of Sfax, Department of Mathematics
  • University of Sfax, Tunisia, Faculty of Sciences of Sfax, Department of Mathematics
autor
  • University of Artois, Artois, France
Bibliografia
  • [1] A. Benzaouia and A. El Hajjaji: Delay-dependent stabilization conditions of controlled positive T-S fuzzy systems with time varying delay. Int. J. of Innovative Computing, Information and Control, 7 (2011), 1533-1548.
  • [2] A. Ben Abdallah, I. Ellouze and M. A. Hammami: Practical stability of nonlinear time-varying cascade systems. J. of Dynamical and Control Systems, 15 (2009), 45-62.
  • [3] A. G. Soldatos and M. Corless: Stabilizing uncertain systems with bounded control. Dynamics and Control, 1 (1991), 227-238.
  • [4] Bassem Ben Hamed, Imen Ellouze and M. A. Hammami: Practical uniform stability of nonlinear differential delay equations. Mediterranean J. of Mathematics, 6 (2010), 139-150.
  • [5] Bassem Ben Hamed and M. A. Hammami: Practical stabilisation of a class of uncertain time-varying nonlinear delay systems. J. of Control Theory and Applications, 7 (2009), 175-180.
  • [6] S. G. Cao, N. W. Ress and G. Feng: Stability analysis and design for class of continuous-time fuzzy control systems. Int. J. of Control, 64 (1996), 1069-1087.
  • [7] G. Feng, S. G. Gao, N. W. Ress and G. K. Chack: Design of fuzzy control systems with guaranteed stability. Fuzzy Sets Systems, 85 (1997), 1-10.
  • [8] J. Park, J. Kim and D. Park: LMI-based design of stabilizing fuzzy controllers for nonlinear systems described by Takagi-Sugeno fuzzy model. Fuzzy Sets Systems, 122 (2003), 73-82.
  • [9] K. Tanaka, T. Ikeda and H. O. Wang: Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory and linear matrix inequalities. IEEE Trans. Fuzzy Systems, 4 (1996), 1-13.
  • [10] Ligang Wu, Xiaojie Su, Peng Shi and Jianbin Qiu: A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems. IEEE Trans. on Systems, Man, and Cybernetics- Part B: Cybernetics, 41 (2011), 273-286.
  • [11] Ligang Wu, Xiaojie Su, Peng Shi and Jianbin Qiu: Model approximation for discrete-time state-delay systems in the T−S fuzzy framework. IEEE Trans. Fuzzy Systems, 19 (2011), 366-378.
  • [12] V. Lakshmikantham, S. Leela and A. A. Martynnyuk: Practical Stability of Nonlinear Systems. World Scientific Singapore, 1990.
  • [13] J. P. Lasalle and S. Lefschetz: Stability by Lyapunov’s Direct Method with Application. Academic Press New York, 1961.
  • [14] Linna Zhou, Qingling Zhang and Chunyu Yang: Practical stability analysis and synthesis of a class of uncertain T-S fuzzy systems. Fuzzy Systems and Knowledge Discovery Lecture Notes in Computer Science, 4223 (2006), 11-20.
  • [15] Liu, Zhang: New approach to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica, 39 (2003), 1571-1582.
  • [16] M. Corless and G. Leitmann: Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems. IEEE Trans. on Automatic Control, 26 (1981), 1139-1143.
  • [17] M. Corless: Guaranteed rates of exponential convergence for uncertain systems. J. of Optimization Theory and Applications, 64 (1990), 481-494.
  • [18] M. Corless and G. Leitmann: Bounded controllers for robust exponential convergence. J. of Optimization Theory and Applications, 76 (1993), 1-12.
  • [19] N. Hadj Taieb, M. A. Hammami, F. Delmotte and M. Ksontini: On the global stabilization of Takagi-Sugeno fuzzy cascaded systems. Nonlinear Dynamics, 67 (2012), 2847-2856.
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  • [21] Tai-Zu Wu and Yau-Tarng Juang: Design of variable structure control for fuzzy nonlinear systems. Expert System with Applications, 35 (2008), 1496-1503.
  • [22] T. Takagi and M. Sugeno: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. on Systems, Man, and Cybernetics- Part B: Cybernetics, 15 (1985), 116-132.
  • [23] R. M. Tong: A control engineering review of fuzzy systems. Automatica, 13 (1977), 559-568.
  • [24] Xiao-Heng Chang and Guang-Hong Yang: Relaxed results on stabilization and state feedback H∞ control conditions for T-S fuzzy systems. Int. J. of Innovative Computing, Information and Control, 7 (2011), 1753-1764.
  • [25] Xiaojie Su, Peng Shi, Ligang Wu and Yong-Duan Song: A novel approach to filter design for T-S fuzzy discrete-time systems with time-varying delay, to appear in IEEE Transactions Fuzzy Systems.
  • [26] H. O. Wang, K. Tanaka and M. Griffin: Parallel distributed compensation of nonlinear systems by Takagi and Sugeno’s model. Proceedings of Fuzzy’95, (1995).
  • [27] H. O. Wang, K. Tanaka and M. Griffin: An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Trans. Fuzzy Systems, 4 (1996), 14-23.
  • [28] W. Tang, G. Chen and R. Lu: A modified fuzzy PI controller for a flexible-joint robot arm with uncertainties. Fuzzy Sets Systems, 118 (2001), 109-119.
  • [29] Wen-Jer Chang, Cheung-Chieh Ku and Pei-Hwa Huang: Robust fuzzy control via observer feedback for passive stochastic fuzzy systems with time-delay and multiplicative noise. Int. J. of Innovative Computing, Information and Control, 7 (2011), 345-364.
  • [30] L. A. Zadeh: Outline of a new approach to the analysis of complex systems and decision process. IEEE Trans. on Systems, Man, and Cybernetics- Part B: Cybernetics, 3 (1973), 28-44.
  • [31] J. M. Zhang, R. H. Li and P. A. Zhang: Stability analysis and systtematic design of fuzzy control systems. Fuzzy Sets Systems, 120 (2001), 65-72.
  • [32] Z. J. Wu, X. J. Xie and S. Y. Zhang: Stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function. Int. J. of Control, 79 (2006), 1635-1646.
  • [33] Z. P. Jiang and L. Praly: Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties. Automatica, 34 (1998), 825-840.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-23c9d8ff-1b66-4eca-a67d-4e0674c8f591
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