×

Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays. (English) Zbl 1144.93018

Summary: We consider delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed delays. Although many kinds of stability conditions for fuzzy systems with discrete delays have already been obtained, almost no stability condition for fuzzy systems with distributed delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed delays. Here we employ a generalized Lyapunov functional to obtain delay-dependent stability conditions of fuzzy systems with discrete and distributed delays. We introduce some free weighting matrices to such a Lyapunov functional in order to reduce the conservatism in stability conditions. These techniques lead to generalized and less conservative stability conditions. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we give two examples to illustrate our results. Delay-dependent stability conditions obtained here are shown to guarantee a wide stability region.

MSC:

93C42 Fuzzy control/observation systems
93D09 Robust stability
93C41 Control/observation systems with incomplete information
93D30 Lyapunov and storage functions
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cao, Y.-Y.; Frank, P. M., Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach, IEEE Transactions on Fuzzy Systems, 8, 200-211 (2000)
[2] Cao, Y.-Y.; Frank, P. M., Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models, Fuzzy Sets and Systems, 124, 213-229 (2001) · Zbl 1002.93051
[3] Chen, J. D.; Lien, C. H.; Fan, K. K.; Cheng, J. S., Delay-dependent criteria for neutral time-delay systems, Electronics Letters, 36, 1897-1898 (2000)
[4] Chen, J. D.; Lien, C. H.; Fan, K. K.; Chou, J. H., Criteria for asymptotic stability of a class of neutral systems via a LMI approach, IEEE Proceedings Control Theory Applied, 148, 442-447 (2001)
[5] Gu, K.; Niculescu, S.-I., Additional dynamics in transformed time-delay systems, IEEE Transaction on Automatic Control, 45, 572-575 (2000) · Zbl 0986.34066
[6] Gu, K.; Niculescu, S.-I., Further remarks on additional dynamics in various model transformations of linear delay systems, IEEE Transaction on Automatic Control, 46, 497-500 (2001) · Zbl 1056.93511
[7] Guan, X. P.; Chen, C. L., Delay-dependent guaranteed cost control for T-S fuzzy systems with time-delay, IEEE Transaction on Fuzzy Systems, 12, 236-249 (2004) · Zbl 1142.93363
[8] Han, Q.-L., A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays, Automatica, 40, 1791-1796 (2004) · Zbl 1075.93032
[9] Hua, C.; Li, F.; Guan, X., Observer-based adaptive control for uncertain time-delay systems, Information Sciences, 176, 201-214 (2006) · Zbl 1121.93034
[10] Lee, K. R.; Kim, J. H.; Jeung, E. T.; Park, H. B., Output feedback \(H_\infty\) control of uncertain fuzzy dynamic systems with time-varying delay, IEEE Transactions on Fuzzy Systems, 8, 657-664 (2000)
[11] Li, C.; Wang, H.; Liao, X., Delay-dependent robust stability of uncertain fuzzy systems with time-varying delays, IEE Proceedings on Control Theory Applications, 151, 417-421 (2004)
[12] Park, J. H., Design of a dynamic output feedback controller for a class of neutral systems with discrete and distributed delays, IEEE Proceedings Control Theory Applied, 151, 610-614 (2004)
[13] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Transaction on Systems, Man, Cybernetics, 15, 116-132 (1985) · Zbl 0576.93021
[14] Tanaka, K.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy Sets and Systems, 45, 135-156 (1992) · Zbl 0758.93042
[15] Teixiera, M. C.M.; Assuncao, E.; Avellar, R. G., On relaxed LMI-based designs for fuzzy regulators and fuzzy observers, 11, 613-623 (2003)
[16] Tian, E.; Pang, C., Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay, Fuzzy Sets and Systems, 157, 544-559 (2006) · Zbl 1082.93031
[17] Ting, C.-S., An observer-based approach to controlling time-delay chaotic systems via Takagi-Sugeno fuzzy model, Information Sciences, 177, 4314-4328 (2007) · Zbl 1120.93037
[18] Tuan, H. D.; Apkarian, P.; Narikiyo, T.; Yamamoto, Y., Parameterized linear matrix inequality techniques in fuzzy control system design, IEEE Transactions on Fuzzy Systems, 9, 324-332 (2001)
[19] Wu, M.; He, Y.; She, J.-H., New delay-dependent stability criteria and stabilizing method for neutral systems, IEEE Transactions on Automatic Control, 49, 2266-2271 (2004) · Zbl 1365.93358
[20] Xie, L., Output feedback \(H_\infty\) control of systems with parameter uncertainty, International Journal of Control, 63, 741-759 (1996)
[21] Xie, L.; Fridman, E.; Shaked, U., Robust \(H_\infty\) control of distributed delay systems with application to combustion control, IEEE Transactions on Automatic Control, 46, 1930-1935 (2001) · Zbl 1017.93038
[22] J. Yoneyama, Robust control analysis and synthesis for uncertain fuzzy systems with time-delays, in: IEEE International Conference on Fuzzy Systems, St. Luis, USA, May, 2003, pp. 396-401.; J. Yoneyama, Robust control analysis and synthesis for uncertain fuzzy systems with time-delays, in: IEEE International Conference on Fuzzy Systems, St. Luis, USA, May, 2003, pp. 396-401.
[23] J. Yoneyama, Stability and stabilization of fuzzy time-delay systems, in: 5th Asian Control Conference, Melbourne, Australia, 2004, pp. 1518-1525.; J. Yoneyama, Stability and stabilization of fuzzy time-delay systems, in: 5th Asian Control Conference, Melbourne, Australia, 2004, pp. 1518-1525.
[24] J. Yoneyama, Generalized stability conditions for Takagi-Sugeno fuzzy time-delay systems, in: IEEE International Conference on Intelligent Systems, Singapore, 2004, pp. 491-496.; J. Yoneyama, Generalized stability conditions for Takagi-Sugeno fuzzy time-delay systems, in: IEEE International Conference on Intelligent Systems, Singapore, 2004, pp. 491-496.
[25] J. Yoneyama, New generalized stability conditions for Takagi-Sugeno fuzzy time-delay systems, in: 2005 IEEE International Conference on Fuzzy Systems, Reno, USA, 2005, pp. 957-962.; J. Yoneyama, New generalized stability conditions for Takagi-Sugeno fuzzy time-delay systems, in: 2005 IEEE International Conference on Fuzzy Systems, Reno, USA, 2005, pp. 957-962.
[26] J. Yoneyama, Robust stability and stabilization for fuzzy systems with discrete and distributed delays, in: IEEE International Symposium on Intelligent Systems, Munich, Germany, 2006, pp. 2372-2377.; J. Yoneyama, Robust stability and stabilization for fuzzy systems with discrete and distributed delays, in: IEEE International Symposium on Intelligent Systems, Munich, Germany, 2006, pp. 2372-2377.
[27] Yoneyama, J., New delay-dependent approach to robust stability and stabilization for Takagi-Sugeno fuzzy time-delay systems, Fuzzy Sets and Systems, 158, 2225-2237 (2007) · Zbl 1122.93050
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.