On the global stabilization of perturbed nonlinear fuzzy control systems

Document Type : Research Paper

Authors

1 Department of Mathematics, IPEIS, University of Sfax, Tunisia

2 Department of Mathematics, Faculty of Sciences, University of Sfax, Tunisia

Abstract

In this paper, we deal with the global practical exponential stabilization of a class of perturbed Takagi-Sugeno fuzzy control systems. The terms of perturbations are supposed uniformly  bounded by some known  functions and in certain cases not necessarily smooth. We prove that the solution of the closed-loop system with a linear fuzzy controller converge
to  a neighborhood of the origin. We use common quadratic Lyapunov function  and parallel distributed compensation controller techniques to study the asymptotic behavior of the solutions of fuzzy system. Numerical simulations are given to validate the proposed approach.

Keywords

References

[1] A. Ben Abdallah, I. Ellouze, M. A. Hammami, Practical stability of nonlinear time-varying cascade systems, Journal of Dynamical and Control Systems, 15 (2009), 45-62.
[2] A. Ben Abdallah, I. Ellouze, M. A. Hammami, Practical exponential stability of perturbed triangular systems and a separation principle, Asian Journal of Control, 13 (2011), 445-448.
[3] H. Ben Zina, M. Bouattour, M. Chaabane, Robust Takagi-Sugeno sensor fault tolerant control strategy for nonlinear system, Iranian Journal of Fuzzy Systems, 6 (2019), 177-189.
[4] T. Caraballo, M. A. Hammami, L. Mchiri, Practical stability of stochastic delay evolution equations, Acta Applicandae Mathematicae, 142 (2016), 91-105.
[5] T. Caraballo, M. A. Hammami, L. Mchiri, Practical exponential stability of impulsive stochastic functional differential equations, Systems and Control Letters, 109 (2017), 43-48.
[6] N. Hadj Taieb, Stability an analysis for time-varying nonlinear systems, International Journal of Control, 9 (2022), 1497-1506.
[7] N. Hadj Taieb, M. A Hammami, Some new results on the global uniform asymptotic stability of time-varying dynamical systems, IMA Journal of Mathematical and Control Information, 32 (2017), 1-22.
[8] N. Hadj Taieb, M. A. Hammami, F. Delmotte, Stabilization of a certain class of fuzzy control systems with uncertainties, Archives of Control Sciences, 3 (2017), 453-481.
[9] N. Hadj Taieb, M. A. Hammami, F. Delmotte, A separation principle for Takagi-Sugeno control fuzzy systems, Archives of Control Sciences, 29 (2019), 227-245.
[10] B. Hamed, I. Ellouze, M. A. Hammami, Practical uniform stability of nonlinear differential delay equations, Mediterranean Journal of Mathematics, 6 (2010), 139-150.
[11] B. Hamed, M. A. Hammami, Practical stabilisation of a class of uncertain time-varying nonlinear delay systems, Journal of Control Theory and Applications, 7 (2009), 175-180.
[12] M. A. Hammami, M. De La Sen, On the uniform exponential stability of time-varying systems subject to discrete time-varying delays and nonlinear delayed perturbations, Mathematical Problems in Engineering, 2015(1) (2015), 12 pages. DOI:10.1155/2015/641268.
[13] A. Hamzaoui, N. Hadj Taieb, M. A. Hammami, Practical partial stability of time-varying systems, Discrete and Continuous Dynamical Systems-B, 7 (2022), 3585-3603.
[14] D. Huang, S. K. Nguang, Robust H∞ static output feedback control of fuzzy systems: An LMI approach, IEEE Transactions on Systems, Man, and Cybernetics, Part B, 36 (2006), 216-222.
[15] H. J. Lee, J. B. Park, G. Chen, Robust fuzzy control of nonlinear systems with parameter uncertainties, IEEE Transactions on Fuzzy Systems, 9 (2001), 369-379.
[16] X. D. Liu, Q. L. Zhang, New approach to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI, Automatica, 39 (2003), 1571-1582.
[17] X. Nian, J. Feng, Guaranteed-cost control of a linear uncertain system with multiple time-varying delays: An LMI approach, IEE Proceedings D (Control Theory and Applications), 150 (2003), 17-22.
[18] J. Park, J. Kim, D. Park, LMI-based design of stabilizing fuzzy controllers for nonlinear systems described by Takagi-Sugeno fuzzy model, Fuzzy Sets and Systems, 122 (2003), 73-82.
[19] T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man, and Cybernetics, Part B, 15 (1985), 116-132.
[20] S. Tong, T. Wang, H. X. Li, Fuzzy robust tracking control for uncertain nonlinear systems, International Journal of Approximate Reasoning, 30 (2002), 73-90.
[21] C. S. Tseng, B. S. Chen, H. J. Uang, Fuzzy tracking control design for nonlinear dynamics systems via T-S fuzzy model, IEEE Transactions on Fuzzy Systems, 9 (2022), 381-392.
[22] J. M. Zhang, R. H. Li, P. A. Zhang, Stability analysis and systtematic design of fuzzy control systems, Fuzzy Sets and Systems, 120 (2001), 65-72.
Iranian Journal of Fuzzy Systems
Volume 20, Issue 1
January and February 2023
Pages 39-52

Files

Share

How to cite

Statistics