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Passivity and passification of fuzzy systems with time delays. (English) Zbl 1122.93368

Summary: Takagi-Sugeno (T-S) fuzzy model provides an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output submodels. Recently, a number of authors studied the T-S fuzzy systems with time delays. In this paper, the passivity and feedback passification of T-S fuzzy systems with time delays are considered. Both delay-independent and delay-dependent results are presented, and the theoretical results are given in terms of linear matrix inequalities (LMIs). Numerical examples are given which illustrate the effectiveness of the theoretical results.

MSC:

93C42 Fuzzy control/observation systems
93D15 Stabilization of systems by feedback
34K06 Linear functional-differential equations
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[1] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE trans. syst. man. cybern., 15, 116-132, (1985) · Zbl 0576.93021
[2] Cao, Y.Y.; Frank, P.M., Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach, IEEE trans. fuzzy systems, 8, 2, 200-211, (2000)
[3] 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
[4] Lee, K.R.; Kim, J.H.; Jeung, E.T.; Park, H.B., Output feedback H∞ control of uncertain fuzzy dynamic systems with time-varying delay, IEEE trans. fuzzy systems, 8, 6, 657-664, (2000)
[5] Zhang, Y.; Heng, P.A., Stability of fuzzy control systems with bounded uncertain delays, IEEE trans. fuzzy systems, 10, 1, 92-97, (2002) · Zbl 1142.93377
[6] Guan, X.-P.; Chen, C.-L., Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays, IEEE trans. fuzzy ststems, 12, 2, 236-249, (2004) · Zbl 1142.93363
[7] Wang, Z.; Ho, D.W.C.; Liu, X., A note on the robust stability of uncertain stochastic fuzzy systems with time-delays, IEEE trans. SMC-A, 34, 4, 570-576, (2004)
[8] Li, C.; Wang, H.; Liao, X., Delay-dependent robust stability of uncertain fuzzy systems with time- varying delays, IEE proc. -contr. theor. appl., 151, 417-421, (2004)
[9] Li, C.; Liao, X.; Wang, H., Stability analysis of fuzzy large-scale systems with time delays in interconnections, International journal of general systems, 33, 6, 621-633, (2004) · Zbl 1155.93380
[10] Bevelevich, V., Classical network synthesis, (1968), Van Nostrand New York
[11] Willems, J.C., Dissipative dynamical systems-part I: general theory, Arch. ration. mech. anal., 45, 321-351, (1972) · Zbl 0252.93002
[12] Willems, J.C., Dissipative dynamical systems-part II: linear systems with quadratic supply rates, Arch. ration. mech. anal., 45, 352-393, (1972) · Zbl 0252.93003
[13] Hill, D.; Moylan, P., The stability of nonlinear dissipative systems, IEEE trans. automat. contr., 21, 708-711, (1976) · Zbl 0339.93014
[14] Vidyasagar, M., Nonlinear systems analysis, (1993), Prentice-Hall Englewood Cliffs, NJ · Zbl 0900.93132
[15] Niculescu, S.-I.; Lozano, R., On the passivity of linear delay systems, IEEE trans. auto. contr., 46, 3, 460-464, (2001) · Zbl 1056.93610
[16] Fridman, E.; Shaked, U., On delay-dependent passivity, IEEE trans. auto. contr., 47, 4, 664-669, (2002) · Zbl 1364.93370
[17] Mahmoud, M.S.; Ismail, A., Passivity and passification of time-delay systems, J. math. anal. appl., 292, 247-258, (2004) · Zbl 1084.93014
[18] Li, C.; Liao, X., Passivity analysis of neural networks with time delay, IEEE trans. circuits and systems-II, 52, 8, 471-475, (2005)
[19] Calcev, G., Some remarks on the stability of mamdani fuzzy control systems, IEEE trans. fuzzy systems, 6, 3, 436-442, (1998)
[20] Calcev, G., Passivity approach to fuzzy control systems, Automatica, 33, 3, 339-344, (1998) · Zbl 0919.93047
[21] Li, C.; Zhang, H.; Liao, X., Passivity and passification of uncertain fuzzy systems, IEE proc-circuits device and systems, 152, 6, 649-653, (2005)
[22] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004
[23] Lozano, R.; Brogliato, B.; Egeland, O.; Maschke, B., Dissipative systems analysis and control: theory and applications, (2000), Springer-verlag London · Zbl 0958.93002
[24] Moon, Y.S.; Park, P.; Kwon, W.H.; Lee, Y.S., Delay-dependent robust stabilization of uncertain state- delayed systems, Int. J. control, 74, 14, 1447-1455, (2001) · Zbl 1023.93055
[25] Tanaka, K.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy sets and systems, 45, 135-156, (1992) · Zbl 0758.93042
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