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Yu, Guanjie; Zhang, Hongbin; Huang, Qiong; Dang, Chuangyin

New delay-dependent stability analysis for fuzzy time-delay interconnected systems. (English) Zbl 1284.93256

Int. J. Gen. Syst. 42, No. 7, 739-753 (2013).
Summary: This paper investigates the delay-dependent stability of continuous-time fuzzy interconnected systems with time-varying delays. The fuzzy interconnected system consists of \(N\) interconnected continuous-time Takagi-Sugeno fuzzy subsystems. A stability criterion based on fuzzy Lyapunov-Krasovskii functional is proposed to guarantee the asymptotic stability of fuzzy time-delay interconnected systems. In the derivation process, some free fuzzy weighting matrices are introduced among the terms of the system equation to yield less conservative results. The proposed stability criterion can be obtained by solving a set of linear matrix inequalities that are numerically feasible. Finally, two numerical examples are provided to demonstrate the effectiveness of the present method.

Cited in 2 Documents

MSC:

93E15 Stochastic stability in control theory
93D20 Asymptotic stability in control theory
93C42 Fuzzy control/observation systems
93C15 Control/observation systems governed by ordinary differential equations

Keywords:

fuzzy interconnected systems; stability; time-delay; linear matrix inequalities (LMIs); Takagi-Sugeno model
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References:

[1] Baiios J. C. M., IEEE transactions on automatic control 40 (5) pp 971– (1995) · Zbl 0825.93027 · doi:10.1109/9.384243
[2] Boyd S., Linear Matrix Inequalities in Systems and Control Theory (SIAM Studies in Applied Mathematics) (1994) · Zbl 0816.93004 · doi:10.1137/1.9781611970777
[3] DOI: 10.1109/91.842153 · doi:10.1109/91.842153
[4] Chen B., IEEE Transactions on Fuzzy Systems 13 (2) pp 238– (2005) · doi:10.1109/TFUZZ.2004.840131
[5] Chiang H. D., IEE Proceedings D Control Theory and Applications 139 (1) pp 79– (1992) · Zbl 0763.93003 · doi:10.1049/ip-d.1992.0012
[6] Hou Y. Y., International Journal of General Systems 38 (5) pp 485– (2009) · Zbl 1184.93082 · doi:10.1080/03081070902753697
[7] Hsiao F. H., IEEE Transactions on Circuits and Systems 52 (9) pp 1883– (2005) · doi:10.1109/TCSI.2005.852492
[8] Hsiao F. H., IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics 32 (1) pp 122– (2002) · doi:10.1109/3477.979967
[9] Hu Z. Z., IEEE Transactions on Automatic Control 39 (1) pp 180– (1994) · Zbl 0796.93007 · doi:10.1109/9.273363
[10] Johansson M., IEEE Transactions on Fuzzy Systems 7 (6) pp 713– (1999) · doi:10.1109/91.811241
[11] Lam H. K., IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics 35 (6) pp 1322– (2005) · doi:10.1109/TSMCB.2005.850181
[12] DOI: 10.1016/j.chaos.2005.08.077 · Zbl 1142.93366 · doi:10.1016/j.chaos.2005.08.077
[13] Shin H., Fuzzy Optimization and Decision Making 3 (1) pp 83– (2004) · Zbl 1084.93015 · doi:10.1023/B:FODM.0000013073.24535.7d
[14] DOI: 10.1109/TSMC.1985.6313399 · Zbl 0576.93021 · doi:10.1109/TSMC.1985.6313399
[15] DOI: 10.1109/TFUZZ.2003.814861 · doi:10.1109/TFUZZ.2003.814861
[16] DOI: 10.1109/TSMCB.2003.818437 · doi:10.1109/TSMCB.2003.818437
[17] DOI: 10.1109/TFUZZ.2004.825975 · Zbl 1331.93011 · doi:10.1109/TFUZZ.2004.825975
[18] DOI: 10.1109/91.481841 · doi:10.1109/91.481841
[19] Yi Z., IEEE Transactions on Fuzzy Systems 10 (1) pp 92– (2002) · Zbl 1142.93377 · doi:10.1109/91.983283
[20] DOI: 10.1016/j.fss.2004.04.015 · Zbl 1083.93014 · doi:10.1016/j.fss.2004.04.015
[21] DOI: 10.1109/TSMC.1973.5408575 · Zbl 0273.93002 · doi:10.1109/TSMC.1973.5408575
[22] Zhang H. B., IEEE Transactions on Fuzzy Systems 16 (6) pp 1649– (2008) · doi:10.1109/TFUZZ.2008.2004999
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