zbMATH — the first resource for mathematics

Reliable guaranteed cost control for uncertain fuzzy neutral systems. (English) Zbl 1203.93114
Summary: This paper focuses on the problem of robust reliable guaranteed cost control for a class of uncertain Takagi-Sugeno fuzzy neutral systems with linear fractional parametric uncertainties. The aim is to design a state feedback controller such that, for all admissible uncertainties as well as actuator failures occurring among the prespecified subset of actuators, the plant remains asymptotically stable and guarantees an adequate level of a quadratic cost index. Based on the Lyapunov-Krasovskii functional, the Barbalat lemma, the descriptor system approach and the free weighting matrix method, new delay-dependent sufficient conditions for solvability of this problem are presented in terms of linear matrix inequalities. Based on that, the design problem of the optimal reliable guaranteed cost controller is formulated as a convex optimization problem. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.

MSC:
 93C42 Fuzzy control/observation systems 93D09 Robust stability 93D15 Stabilization of systems by feedback 93D20 Asymptotic stability in control theory 90C25 Convex programming
Full Text:
References:
 [1] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE trans. syst. man cybern., 15, 1, 116-132, (1985) · Zbl 0576.93021 [2] Cao, S.G.; Rees, N.W.; Feng, G., Analysis and design of a class of continuous time fuzzy control systems, Internat. J. control, 64, 1069-1087, (1996) · Zbl 0867.93053 [3] Kim, E.; Lee, H., New approaches to relaxed quadratic stability condition of fuzzy control systems, IEEE trans. fuzzy syst., 8, 5, 523-534, (2000) [4] Liu, X.; Zhang, Q.L., New approaches to controller designs based on fuzzy observers for T-S fuzzy systems via LMI, Automatica, 39, 1571-1582, (2003) · Zbl 1029.93042 [5] Hale, J.K., Theory of functional differential equations, (1977), Springer New York [6] Cao, Y.Y.; Frank, P.M., Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach, IEEE trans. fuzzy syst., 8, 2, 200-211, (2000) [7] Jiang, X.F.; Han, Q.L., Robust $$H_\infty$$ control for uncertain takagi – sugeno fuzzy systems with interval time-varying delay, IEEE trans. fuzzy syst., 15, 2, 321-331, (2007) [8] Liu, X., Delay-dependent $$H_\infty$$ control for uncertain fuzzy systems with time-varying delays, Nonlinear anal., 68, 5, 1352-1361, (2008) · Zbl 1137.93021 [9] Kolmanovskii, V.; Myshkis, A., Applied theory of functional differential equations, (1992), Kluwer Academic Publishers Netherlands · Zbl 0917.34001 [10] Chen, W.H.; Zheng, W.X., Delay-dependent robust stabilization for uncertain neutral systems with distributed delays, Automatica, 43, 1, 95-104, (2007) · Zbl 1140.93466 [11] Han, Q.L., A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays, Automatica, 40, 10, 1791-1796, (2004) · Zbl 1075.93032 [12] Park, J.H., Delay-dependent guaranteed cost stabilization criterion for neutral delay-differential systems: matrix inequality approach, Comput. math. appl., 47, 1507-1515, (2004) · Zbl 1070.34106 [13] Xu, S.Y.; Lam, J.; Chen, B., Robust $$H_\infty$$ control for uncertain fuzzy neutral delay systems, Eur. J. control, 10, 365-380, (2004) · Zbl 1293.93661 [14] J. Yoneyama, Generalized conditions for $$H_\infty$$ disturbance attenuation of fuzzy time-delay systems, IEEE Int. Conf. on Syst., Man and Cybern., 2005, pp. 1736-1741. [15] Li, Y.; Xu, S.; Zhang, B.; Chu, Y., Robust stabilization and $$H_\infty$$ control for uncertain fuzzy neutral systems with mixed time delays, Fuzzy sets and systems, 159, 20, 2730-2748, (2008) · Zbl 1170.93343 [16] Yang, J.; Zhong, S.M.; Xiong, L.L., A descriptor system approach to non-fragile $$H_\infty$$ control for uncertain fuzzy neutral systems, Fuzzy sets and systems, 160, 423-438, (2009) · Zbl 1175.93136 [17] Yang, J.; Zhong, S.M.; Li, G.H.; Luo, W.P, Robust $$H_\infty$$ filter design for uncertain fuzzy neutral systems, Inform. sci., 179, 3697-3710, (2009) · Zbl 1171.93351 [18] Chang, S.; Peng, T., Adaptive guaranteed cost control of systems with uncertain parameters, IEEE trans. automat. control, AC-17, 474-483, (1972) · Zbl 0259.93018 [19] Chen, B.; Liu, X.P., Fuzzy guaranteed cost control for nonlinear systems with time-varying delay, IEEE trans. fuzzy syst., 13, 2, 238-249, (2005) [20] Chen, B.; Liu, X.P.; Tong, S.C.; Lin, C., Guaranteed cost control of T-S fuzzy systems with state and input delays, Fuzzy sets and systems, 158, 2251-2267, (2007) · Zbl 1122.93049 [21] Guan, X.P.; Chen, C.L., Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays, IEEE trans. fuzzy syst., 12, 2, 236-249, (2004) · Zbl 1142.93363 [22] Jiang, X.; Han, Q.L., On guaranteed cost fuzzy control for nonlinear systems with interval time-varying delay, IET control theory appl., 1, 6, 1700-1710, (2007) [23] Chen, B.; Liu, X.P., Reliable control design of fuzzy dynamic systems with time-varying delay, Fuzzy sets and systems, 146, 349-374, (2004) · Zbl 1055.93050 [24] Wang, Y.Q.; Liu, L.H.; Zhou, D.H., Reliable memory feedback design for a class of nonlinear fuzzy systems with time-varying delay, Fault detection, supervision safety techn. process., 2006, 753-758, (2007) [25] Wang, Z.; Huang, B.; Unbehauen, H., Robust reliable control for a class of uncertain nonlinear state delayed systems, Automatica, 35, 5, 955-963, (1999) · Zbl 0945.93605 [26] Wu, H.N., Reliable LQ fuzzy control for nonlinear discrete-time systems via lmis, IEEE trans. syst., man cybern. part B, 34, 2, 1270-1275, (2004) [27] Wu, H.N.; Zhang, H.Y., Reliable mixed fuzzy static output feedback control for nonlinear systems with sensor faults, Automatica, 41, 11, 1925-1932, (2005) · Zbl 1086.93034 [28] Wu, H.N.; Zhang, H.Y., Reliable $$H_\infty$$ fuzzy control for a class of discrete-time nonlinear systems using multiple fuzzy Lyapunov functions, IEEE trans. circuits syst. II: express briefs, 54, 4, 357-361, (2007) [29] H.L. Liu, G.R. Duan, Y. Zhang, Robust reliable guaranteed cost control of linear descriptor time-delay systems with actuator failures, in: Proceedings of the Fifth Int. Conf. on Machine Learning and Cybernetics, Dalian, 2006, pp. 422-427. [30] Pujol, G.; Rodellar, J.; Rossell, J.M.; Pozo, F., Decentralised reliable guaranteed cost control of uncertain systems: an LMI design, IET control theory appl., 1, 3, 779-785, (2007) [31] Yang, G.H.; Wang, J.L.; Soh, Y.C., Reliable guaranteed cost control for uncertain nonlinear systems, IEEE trans. automat. control, 45, 11, 2188-2192, (2000) · Zbl 0991.93035 [32] Yu, L., An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure, Appl. math. comput., 162, 1325-1331, (2005) · Zbl 1125.93046 [33] K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proc. of the 39th IEEE Conf. on Decision and Control, 2000, pp. 2805-2810. [34] Tuan, H.D.; Apkarian, P.; Narikiyo, T.; Yamamoto, Y., Parameterized linear matrix inequality techniques in fuzzy control system design, IEEE trans. fuzzy syst., 9, 2, 324-332, (2001) [35] Xie, L., Output feedback $$H_\infty$$ control of systems with parameter uncertainty, Internat. J. control, 63, 4, 741-750, (1996) · Zbl 0841.93014 [36] Cao, Y.Y.; Lin, Z., Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation, IEEE trans. fuzzy syst., 11, 1, 57-67, (2003) [37] Khargoneker, P.P.; Petersen, I.R.; Zhou, K., Robust stabilization of uncertain linear systems: quadratic stabilizability and control theory, IEEE trans. automat. control, 35, 3, 356-361, (1990) · Zbl 0707.93060 [38] Zhou, S.; Feng, G.; Lam, J.; Xu, S., Robust $$H_\infty$$ control for discrete-time fuzzy systems via basis-dependent Lyapunov functions, Inform. sci., 174, 197-217, (2005) · Zbl 1113.93038
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.