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Passivity analysis and passive control of fuzzy systems with time-varying delays. (English) Zbl 1221.93063

Summary: This paper is concerned with the passive controller design problem for a class of continuous-time Takagi-Sugeno (T-S) fuzzy systems with both state and input delays. The delays are assumed to be time-varying and differentiable. A notion of very-strict passivity is adopted. The purpose is to design a state-feedback fuzzy controller such that the resulting closed-loop system is Very-Strictly Passive (VSP). Delay-dependent conditions for the solvability of the addressed problem are obtained by applying recently developed techniques for time-delay systems and fuzzy systems. These conditions are expressed by means of strict Linear Matrix Inequalities (LMIs) that can be easily solved. A numerical example and simulation results are provided to demonstrate the effectiveness of the proposed method.

MSC:

93B35 Sensitivity (robustness)
93C42 Fuzzy control/observation systems
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[1] Bemporad, A.; Bianchini, G.; Brogi, F., Passivity analysis and passification of discrete-time hybrid systems, IEEE transactions on automatic control, 53, 4, 1004-1009, (2008) · Zbl 1367.93337
[2] Bernal, M.; Guerra, T.M.; Kruszewski, A., A membership-function-dependent approach for stability analysis and controller synthesis of takagi – sugeno models, Fuzzy sets and systems, 160, 2776-2795, (2009) · Zbl 1176.93042
[3] Cao, Y.Y.; Frank, P.M., Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach, IEEE transactions on fuzzy systems, 8, 2, 200-211, (2000)
[4] 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
[5] Delmotte, F.; Guerra, T.M.; Kruszewski, A., Discrete takagi – sugeno’s fuzzy models: reduction of the number of LMI in fuzzy control techniques, IEEE transactions on systems, man, and cybernetics—B: cybernetics, 38, 5, 1423-1427, (2008)
[6] Chen, B.; Liu, X.; Lin, C.; Liu, K., Robust \(H_\infty\) control of takagi – sugeno fuzzy systems with state and input time delays, Fuzzy sets and systems, 160, 403-422, (2009) · Zbl 1175.93119
[7] Chen, B.; Liu, X.; Tong, S.; 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
[8] Dong, J.; Yang, G.H., Static output feedback \(H_\infty\) control of a class of nonlinear discrete-time systems, Fuzzy sets and systems, 160, 2844-2859, (2009) · Zbl 1176.93044
[9] Feng, G., A survey on analysis and design of model-based fuzzy control systems, IEEE transactions on fuzzy systems, 14, 5, 676-697, (2006)
[10] Fridman, E.; Shaked, U., On delay-dependent passivity, IEEE transactions on automatic control, 47, 4, 664-669, (2002) · Zbl 1364.93370
[11] Gao, H.; Chen, T.; Chai, T., Passivity and passification for networked control systems, SIAM journal on control and optimization, 46, 4, 1299-1322, (2007) · Zbl 1140.93425
[12] Gao, H.; Liu, X.; Lam, J., Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay, IEEE transactions on systems, man, and cybernetics—B: cybernetics, 39, 2, 306-317, (2009)
[13] Gao, H.; Zhao, Y.; Lam, J.; Chen, K., \(H_\infty\) fuzzy filtering of nonlinear systems with intermittent measurements, IEEE transactions on fuzzy systems, 17, 2, 291-300, (2009)
[14] Guerra, T.M.; Vermeiren, L., LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi – sugeno’s form, Automatica, 40, 823-829, (2004) · Zbl 1050.93048
[15] Hill, D.; Moylan, P., The stability of nonlinear dissipative systems, IEEE transactions on automatic control, 21, 5, 708-711, (1976) · Zbl 0339.93014
[16] Lam, J.; Zhou, S., Dynamic output feedback \(H_\infty\) control of discrete-time fuzzy systems: a fuzzy-basis-dependent Lyapunov function approach, International journal of systems science, 38, 1, 25-37, (2007) · Zbl 1111.93017
[17] Lee, K.R.; Kim, J.H.; Jeung, E.T.; Park, H.B., Output feedback robust \(H_\infty\) control of uncertain fuzzy dynamic systems with time-varying delay, IEEE transactions on fuzzy systems, 8, 6, 657-664, (2000)
[18] Li, C.G.; Zhang, H.B.; Liao, X.F., Passivity and passification of fuzzy systems with time delays, Computers and mathematics with applications, 52, 1067-1078, (2006) · Zbl 1122.93368
[19] Li, C.G.; Zhang, H.B.; Liao, X.F., Passivity and passification of uncertain fuzzy systems, IEE Proceedings circuits, device and systems, 152, 6, 649-653, (2005)
[20] Li, H.; Chen, B.; Zhou, Q.; Qian, W., Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters, IEEE transactions on systems, man, and cybernetics—B: cybernetics, 39, 1, 94-102, (2009)
[21] 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, 2730-2748, (2008) · Zbl 1170.93343
[22] Lin, C.; Wang, Q.G.; Lee, T.H., Delay-dependent LMI conditions for stability and stabilization of T-S fuzzy systems with bounded time delay, Fuzzy sets and systems, 157, 1229-1247, (2006) · Zbl 1090.93024
[23] Lin, C.; Wang, Q.G.; Lee, T.H.; He, Y.; Chen, B., Observer-based \(H_\infty\) fuzzy control design for T-S fuzzy systems with state delays, Automatica, 44, 868-874, (2008) · Zbl 1283.93164
[24] Lozano, R.; Brogliato, B.; Egeland, O.; Maschke, B., Dissipative systems analysis and control: theory and applications, (2007), Springer-Verlag London, UK · Zbl 1121.93002
[25] Nguang, S.K.; Shi, P., \(H_\infty\) fuzzy output feedback control design for nonlinear systems: an LMI approach, IEEE transactions on fuzzy systems, 11, 3, 331-340, (2003)
[26] Nguang, S.K.; Shi, P., Fuzzy \(H_\infty\) output feedback control of nonlinear systems under sampled measurements, Automatica, 39, 2169-2174, (2003) · Zbl 1041.93033
[27] Niculescu, S.I.; Lozano, R., On the passivity of linear delay systems, IEEE transactions on automatic control, 46, 3, 460-464, (2001) · Zbl 1056.93610
[28] Tanaka, K.; Wang, H.O., Fuzzy control system design and analysis: A linear matrix inequality approach, (2001), Wiley New York
[29] Tanaka, K.; Ohtake, H.; Wang, H.O., Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach, IEEE transactions on systems, man, and cybernetics—B: cybernetics, 39, 2, 561-567, (2009)
[30] Tian, E.; Yue, D.; Zhang, Y., Delay-dependent robust \(H_\infty\) control for T-S fuzzy system with interval time-varying delay, Fuzzy sets and systems, 160, 1708-1719, (2009) · Zbl 1175.93134
[31] Tong, S.; Wang, W.; Qu, L., Decentralized robust control for uncertain T-S fuzzy large-scale systems with time-delay, International journal of innovative computing, information and control, 3, 657-672, (2007)
[32] Tong, S.; Zhang, Q., Decentralized output feedback fuzzy \(H_\infty\) tracking control for nonlinear interconnected systems with time-delay, International journal of innovative computing, information and control, 4, 3385-3398, (2008)
[33] Xie, L.; Fu, M.; Li, H., Passivity analysis and passification for uncertain signal processing systems, IEEE transactions on signal processing, 46, 9, 2394-2403, (1998)
[34] Xu, S.; Lam, J., Robust \(H_\infty\) control for uncertain discrete-time-delay fuzzy systems via output feedback controllers, IEEE transactions on fuzzy systems, 13, 1, 82-93, (2005)
[35] Xu, S.; Lam, J., A survey of linear matrix inequality techniques in stability analysis of delay systems, International journal of systems science, 39, 12, 1095-1113, (2008) · Zbl 1156.93382
[36] Xu, S.; Song, B.; Lu, J.; Lam, J., Robust stability of uncertain discrete-time singular fuzzy systems, Fuzzy sets and systems, 158, 2306-2316, (2007) · Zbl 1122.93065
[37] Zhang, B.; Xu, S., Delay-dependent robust \(H_\infty\) control for uncertain discrete-time fuzzy systems with time-varying delays, IEEE transactions on fuzzy systems, 17, 4, 809-823, (2009)
[38] Zhang, B.; Lam, J.; Xu, S.; Shu, Z., Robust stabilization of uncertain T-S fuzzy time-delay systems with exponential estimates, Fuzzy sets and systems, 160, 1720-1737, (2009) · Zbl 1175.93200
[39] Zhang, B.; Xu, S.; Zong, G.; Zou, Y., Delay-dependent stabilization for stochastic fuzzy systems with time delays, Fuzzy sets and systems, 158, 2238-2250, (2007) · Zbl 1122.93051
[40] Zhang, H.B.; Shen, Y.; Feng, G., Delay-dependent stability and \(H_\infty\) control for a class of fuzzy descriptor systems with time-delay, Fuzzy sets and systems, 160, 1689-1707, (2009) · Zbl 1175.93138
[41] Zhao, Y.; Gao, H.; Lam, J.; Du, B., Stability and stabilization of delayed T-S fuzzy systems: a delay partitioning approach, IEEE transactions on fuzzy systems, 17, 4, 750-762, (2009)
[42] Zhao, Y.; Lam, J.; Gao, H., Fault detection for fuzzy systems with intermittent measurements, IEEE transactions on fuzzy systems, 17, 2, 398-410, (2009)
[43] Zhou, S.; Lam, J.; Zheng, W.X., Control design for fuzzy systems based on relaxed nonquadratic stability and \(H_\infty\) performance conditions, IEEE transactions on fuzzy systems, 15, 2, 188-199, (2007)
[44] Zhou, S.; Li, T., Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent lyapunov – krasovskii function, Fuzzy sets and systems, 151, 139-153, (2005) · Zbl 1142.93379
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