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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:
93B35Sensitivity (robustness) of control systems
93C42Fuzzy control systems
References:
[1]Bemporad, A.; Bianchini, G.; Brogi, F.: Passivity analysis and passification of discrete-time hybrid systems, IEEE transactions on automatic control 53, No. 4, 1004-1009 (2008)
[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 · doi:10.1016/j.fss.2009.02.005
[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, No. 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 · doi:10.1016/S0165-0114(00)00120-2
[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, No. 5, 1423-1427 (2008)
[6]Chen, B.; Liu, X.; Lin, C.; Liu, K.: Robust H control of Takagi – sugeno fuzzy systems with state and input time delays, Fuzzy sets and systems 160, 403-422 (2009) · Zbl 1175.93119 · doi:10.1016/j.fss.2008.03.024
[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 · doi:10.1016/j.fss.2007.04.012
[8]Dong, J.; Yang, G. H.: Static output feedback H control of a class of nonlinear discrete-time systems, Fuzzy sets and systems 160, 2844-2859 (2009) · Zbl 1176.93044 · doi:10.1016/j.fss.2008.11.025
[9]Feng, G.: A survey on analysis and design of model-based fuzzy control systems, IEEE transactions on fuzzy systems 14, No. 5, 676-697 (2006)
[10]Fridman, E.; Shaked, U.: On delay-dependent passivity, IEEE transactions on automatic control 47, No. 4, 664-669 (2002)
[11]Gao, H.; Chen, T.; Chai, T.: Passivity and passification for networked control systems, SIAM journal on control and optimization 46, No. 4, 1299-1322 (2007) · Zbl 1140.93425 · doi:10.1137/060655110
[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, No. 2, 306-317 (2009)
[13]Gao, H.; Zhao, Y.; Lam, J.; Chen, K.: H fuzzy filtering of nonlinear systems with intermittent measurements, IEEE transactions on fuzzy systems 17, No. 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 · doi:10.1016/j.automatica.2003.12.014
[15]Hill, D.; Moylan, P.: The stability of nonlinear dissipative systems, IEEE transactions on automatic control 21, No. 5, 708-711 (1976) · Zbl 0339.93014 · doi:10.1109/TAC.1976.1101352
[16]Lam, J.; Zhou, S.: Dynamic output feedback H control of discrete-time fuzzy systems: a fuzzy-basis-dependent Lyapunov function approach, International journal of systems science 38, No. 1, 25-37 (2007) · Zbl 1111.93017 · doi:10.1080/00207720601042967
[17]Lee, K. R.; Kim, J. H.; Jeung, E. T.; Park, H. B.: Output feedback robust H control of uncertain fuzzy dynamic systems with time-varying delay, IEEE transactions on fuzzy systems 8, No. 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 · doi:10.1016/j.camwa.2006.03.029
[19]Li, C. G.; Zhang, H. B.; Liao, X. F.: Passivity and passification of uncertain fuzzy systems, IEE Proceedings circuits, device and systems 152, No. 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, No. 1, 94-102 (2009)
[21]Li, Y.; Xu, S.; Zhang, B.; Chu, Y.: Robust stabilization and H control for uncertain fuzzy neutral systems with mixed time-delays, Fuzzy sets and systems 159, 2730-2748 (2008) · Zbl 1170.93343 · doi:10.1016/j.fss.2008.01.030
[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 · doi:10.1016/j.fss.2005.10.001
[23]Lin, C.; Wang, Q. G.; Lee, T. H.; He, Y.; Chen, B.: Observer-based H fuzzy control design for T – S fuzzy systems with state delays, Automatica 44, 868-874 (2008)
[24]Lozano, R.; Brogliato, B.; Egeland, O.; Maschke, B.: Dissipative systems analysis and control: theory and applications, (2007)
[25]Nguang, S. K.; Shi, P.: H fuzzy output feedback control design for nonlinear systems: an LMI approach, IEEE transactions on fuzzy systems 11, No. 3, 331-340 (2003)
[26]Nguang, S. K.; Shi, P.: Fuzzy H output feedback control of nonlinear systems under sampled measurements, Automatica 39, 2169-2174 (2003) · Zbl 1041.93033 · doi:10.1016/S0005-1098(03)00236-X
[27]Niculescu, S. I.; Lozano, R.: On the passivity of linear delay systems, IEEE transactions on automatic control 46, No. 3, 460-464 (2001) · Zbl 1056.93610 · doi:10.1109/9.911424
[28]Tanaka, K.; Wang, H. O.: Fuzzy control system design and analysis: A linear matrix inequality approach, (2001)
[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, No. 2, 561-567 (2009)
[30]Tian, E.; Yue, D.; Zhang, Y.: Delay-dependent robust H control for T – S fuzzy system with interval time-varying delay, Fuzzy sets and systems 160, 1708-1719 (2009) · Zbl 1175.93134 · doi:10.1016/j.fss.2008.10.014
[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 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, No. 9, 2394-2403 (1998)
[34]Xu, S.; Lam, J.: Robust H control for uncertain discrete-time-delay fuzzy systems via output feedback controllers, IEEE transactions on fuzzy systems 13, No. 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, No. 12, 1095-1113 (2008) · Zbl 1156.93382 · doi:10.1080/00207720802300370
[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 · doi:10.1016/j.fss.2007.05.008
[37]Zhang, B.; Xu, S.: Delay-dependent robust H control for uncertain discrete-time fuzzy systems with time-varying delays, IEEE transactions on fuzzy systems 17, No. 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 · doi:10.1016/j.fss.2008.10.015
[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 · doi:10.1016/j.fss.2007.05.011
[40]Zhang, H. B.; Shen, Y.; Feng, G.: Delay-dependent stability and H control for a class of fuzzy descriptor systems with time-delay, Fuzzy sets and systems 160, 1689-1707 (2009) · Zbl 1175.93138 · doi:10.1016/j.fss.2008.09.014
[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, No. 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, No. 2, 398-410 (2009)
[43]Zhou, S.; Lam, J.; Zheng, W. X.: Control design for fuzzy systems based on relaxed nonquadratic stability and H performance conditions, IEEE transactions on fuzzy systems 15, No. 2, 188-199 (2007)
[44]Zhou, S.; Li, T.: Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent Lyapunov – Krasovskiĭ function, Fuzzy sets and systems 151, 139-153 (2005) · Zbl 1142.93379 · doi:10.1016/j.fss.2004.08.014