Volume 14, Issue 4 (Journal of Control, V.14, N.4 Winter 2021)                   JoC 2021, 14(4): 107-118 | Back to browse issues page

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Nasiri A, Baranzadeh A, Rashidi F. Robust H_∞ Output Feedback Control for T-S Fuzzy Systems: A Non-‎monotonic Approach. JoC 2021; 14 (4) :107-118
URL: http://joc.kntu.ac.ir/article-1-652-en.html
1- University of Hormozgan
Abstract:   (4900 Views)
This paper proposes robust H_∞  output feedback control stabilization for uncertain Takagi–Sugeno (T-S) fuzzy systems via linear matrix inequalities (LMIs). In order to reduce the conservatism associated with T-S fuzzy system, a new form of non-monotonic Lyapunov functions is used. In the non-monotonic approach, the monotonic decrease of the Lyapunov function is relaxed which enables it to increase locally but vanish eventually. Based on the non-monotonic Lyapunov function approach, sufficient conditions for the existence of robust H_∞  output feedback control stabilization are derived. The proposed design technique is shown to be less conservative than the existing non-monotonic approach, namely, K -samples variations of Lyapunov function. The effectiveness of the proposed approach is further illustrated via numerical example.
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Type of Article: Research paper | Subject: Special
Received: 2019/02/26 | Accepted: 2019/11/16 | ePublished ahead of print: 2020/10/5 | Published: 2021/02/19

1. [1] A. A. Ahmadi and P. A. Parrilo, "Non-monotonic Lyapunov functions for stability of discrete time nonlinear and switched systems," in 2008 47th IEEE Conference on Decision and Control, 2008, pp. 614-621. [DOI:10.1109/CDC.2008.4739402]
2. [2] M. H. Asemani and V. J. Majd, "A robust H∞ observer-based controller design for uncertain T-S fuzzy systems with unknown premise variables via LMI," Fuzzy Sets and Systems, vol. 212, pp. 21-40, 2013. [DOI:10.1016/j.fss.2012.07.008]
3. [3] W. Assawinchaichote, S. K. Nguang, P. Shi, and E.-K. Boukas, "H∞ fuzzy state-feedback control design for nonlinear systems with D-stability constraints: An LMI approach," Mathematics and Computers in Simulation, vol. 78, pp. 514-531, 2008. [DOI:10.1016/j.matcom.2007.07.002]
4. [4] Y.-J. Chen, M. Tanaka, K. Inoue, H. Ohtake, K. Tanaka, T. M. Guerra, et al., "A nonmonotonically decreasing relaxation approach of Lyapunov functions to guaranteed cost control for discrete fuzzy systems," IET Control Theory & Applications, vol. 8, pp. 1716-1722, 2014. [DOI:10.1049/iet-cta.2013.1132]
5. [5] S. F. Derakhshan and A. Fatehi, "Non-monotonic Lyapunov functions for stability analysis and stabilization of discrete time Takagi-Sugeno fuzzy systems," Int. J. Innov. Comput. Inf. Control, vol. 10, pp. 1567-1586, 2014.
6. [6] S. F. Derakhshan and A. Fatehi, "Non-monotonic robust H2 fuzzy observer-based control for discrete time nonlinear systems with parametric uncertainties," International Journal of Systems Science, vol. 46, pp. 2134-2149, 2015. [DOI:10.1080/00207721.2013.854941]
7. [7] S. F. Derakhshan, A. Fatehi, and M. G. Sharabiany, "Nonmonotonic observer-based fuzzy controller designs for discrete time TS fuzzy systems via LMI," IEEE transactions on cybernetics, vol. 44, pp. 2557-2567, 2014. [DOI:10.1109/TCYB.2014.2310591]
8. [8] G. Feng, "Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions," IEEE Transactions on Fuzzy Systems, vol. 12, pp. 22-28, 2004. [DOI:10.1109/TFUZZ.2003.819833]
9. [9] G. Feng, "A survey on analysis and design of model-based fuzzy control systems," IEEE Transactions on Fuzzy systems, vol. 14, pp. 676-697, 2006. [DOI:10.1109/TFUZZ.2006.883415]
10. [10] T. M. Guerra, A. Kruszewski, and M. Bernal, "Control law proposition for the stabilization of discrete Takagi-Sugeno models," IEEE Transactions on Fuzzy Systems, vol. 17, pp. 724-731, 2008. [DOI:10.1109/TFUZZ.2008.928602]
11. [11] S. H. Kim, "Improved Approach to Robust ${cal H} _infty $ Stabilization of Discrete-Time T-S Fuzzy Systems With Time-Varying Delays," IEEE Transactions on Fuzzy Systems, vol. 18, pp. 1008-1015, 2010. [DOI:10.1109/TFUZZ.2010.2062523]
12. [12] E. Kim and H. Lee, "New approaches to relaxed quadratic stability condition of fuzzy control systems," IEEE Transactions on Fuzzy systems, vol. 8, pp. 523-534, 2000. [DOI:10.1109/91.873576]
13. [13] 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, pp. 606-611, 2008. [DOI:10.1109/TAC.2007.914278]
14. [14] J. Lam and S. Zhou, "Dynamic output feedback H∞ control of discrete-time fuzzy systems: a fuzzy-basis-dependent Lyapunov function approach," International Journal of Systems Science, vol. 38, pp. 25-37, 2007. [DOI:10.1080/00207720601042967]
15. [15] P. S. Sing Kiong Nguang, "HO∞ fuzzy output feedback control design for nonlinear systems: an MI approach," IEEE Trans. Fuzzy Systems, vol. 11, pp. 331-340, 2003. [DOI:10.1109/TFUZZ.2003.812691]
16. [16] M. C. De Oliveira, J. Bernussou, and J. C. Geromel, "A new discrete-time robust stability condition," Systems & control letters, vol. 37, pp. 261-265, 1999. [DOI:10.1016/S0167-6911(99)00035-3]
17. [17] M. C. De Oliveira, J. C. Geromel, and J. Bernussou, "Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems," International Journal of Control, vol. 75, pp. 666-679, 2002. [DOI:10.1080/00207170210140212]
18. [18] V. A. Yakubovich, "Linear matrix inequalities in system and control theory (S. Boyd, LE Ghaoui, E. Feron, and V. Balakrishnan)," SIAM Review, vol. 37, pp. 479-481, 1995. [DOI:10.1137/1037119]
19. [19] T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE transactions on systems, man, and cybernetics, pp. 116-132, 1985. [DOI:10.1109/TSMC.1985.6313399]
20. [20] D. Saifia, M. Chadli, S. Labiod, and T. M. Guerra, "Robust H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions," Asian Journal of Control, 2019. [DOI:10.1002/asjc.1987]
21. [21] A. Nasiri, S. K. Nguang, A. Swain, and D. J. Almakhles, "Reducing Conservatism in an $ H_ {infty} $ Robust State-Feedback Control Design of T-S Fuzzy Systems: A Nonmonotonic Approach," IEEE Transactions on Fuzzy Systems, vol. 26, pp. 386-390, 2017. [DOI:10.1109/TFUZZ.2017.2649580]
22. [22] M. H. Asemani and R. Vatankhah, "NON‐PDC observer‐based T‐S fuzzy tracking controller design and its application in CHAOS control," Asian Journal of Control, vol. 19, pp. 969-982, 2017. [DOI:10.1002/asjc.1451]
23. [23] B. El Haiek, A. Hmamed, A. El Hajjaji, and E. H. Tissir, "Improved results on observer-based control for discrete-time fuzzy systems," International Journal of Systems Science, vol. 48, pp. 2544-2553, 2017. [DOI:10.1080/00207721.2017.1324067]
24. [24] H. D. Tuan, P. Apkarian, T. Narikiyo, and Y. Yamamoto, "Parameterized linear matrix inequality techniques in fuzzy control system design," IEEE Transactions on fuzzy systems, vol. 9, pp. 324-332, 2001. [DOI:10.1109/91.919253]
25. [25] W.-J. Wang, Y.-J. Chen, and C.-H. Sun, "Relaxed stabilization criteria for discrete-time T-S fuzzy control systems based on a switching fuzzy model and piecewise Lyapunov function," IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 37, pp. 551-559, 2007. [DOI:10.1109/TSMCB.2006.887434]
26. [26] I. R. Petersen and C. V. Hollot, "A Riccati equation approach to the stabilization of uncertain linear systems," Automatica, vol. 22, pp. 397-411, 1986. [DOI:10.1016/0005-1098(86)90045-2]
27. [27] L. Xie, "Output feedback H∞ control of systems with parameter uncertainty," International Journal of control, vol. 63, pp. 741-750, 1996. [DOI:10.1080/00207179608921866]

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