zbMATH — the first resource for mathematics

Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach. (English) Zbl 1237.93156
Summary: This paper focuses on the stability analysis for uncertain Takagi–Sugeno (T–S) fuzzy systems with interval time-varying delay. The uncertainties of system parameter matrices are assumed to be time-varying and norm-bounded. Some new Lyapunov–Krasovskii functionals (LKFs) are constructed by nonuniformly dividing the whole delay interval into multiple segments and choosing different Lyapunov functionals to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the nominal and uncertain T–S fuzzy systems in a convex way. These stability criteria are derived that depend on both the upper and lower bounds of the time derivative of the delay. By employing the new delay partitioning approach, the obtained stability criteria are stated in terms of Linear Matrix Inequalities (LMIs). They are equivalent or less conservative while involving less decision variables than the existing results. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results.

93D20 Asymptotic stability in control theory
93C42 Fuzzy control/observation systems
Full Text: DOI
[1] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its application to modeling and control, IEEE transactions on systems, man, and cybernetics, 15, 116-132, (1985) · Zbl 0576.93021
[2] Teixeira, M.C.; Zak, S.H., Stabilizing controller design for uncertain nonlinear systems using fuzzy models, IEEE transactions on fuzzy systems, 7, 133-144, (1999)
[3] Chen, B.S.; Tseng, C.S.; Uang, H.J., Mixed \(\operatorname{H} 2 / \operatorname{H} \infty\) fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach, IEEE transactions on fuzzy systems, 8, 249-265, (2000)
[4] Akar, M.; Ozguner, U., Decentralized techniques for the analysis and control of takagi – sugeno fuzzy systems, IEEE transactions on fuzzy systems, 8, 691-704, (2000)
[5] Gu, K.; Kharitonov, V.L.; Chen, J., Stability of time-delay systems, (2003), Birkhauser Basel · Zbl 1039.34067
[6] 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, 9, 1229-1247, (2006) · Zbl 1090.93024
[7] Wu, H.N.; Li, H.X., New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay, IEEE transactions on fuzzy systems, 15, 482-493, (2007)
[8] Lien, C.H.; Yu, K.W.; Chen, W.D.; Wan, Z.L.; Chung, Y.J., Stability criteria for uncertain takagi – sugeno fuzzy systems with interval time-varying delay, IET control theory and applications, 1, 764-769, (2007)
[9] Chen, B.; Liu, X.P.; Tong, S.C., New delay-dependent stabilization conditions of T-S systems with constant delay, Fuzzy sets and systems, 158, 2209-2224, (2007) · Zbl 1122.93048
[10] Yoneyama, J., New delay-dependent approach to robust stability and stabilization for takagi – sugeno fuzzy time-delay systems, Fuzzy sets and systems, 158, 2225-2337, (2007) · Zbl 1122.93050
[11] Peng, C.; Tian, Y.C.; Tian, E.G., Improved delay-dependent robust stabilization conditions of uncertain T-S fuzzy systems with time-varying delay, Fuzzy sets and systems, 159, 2713-2729, (2008) · Zbl 1170.93344
[12] Li, L.; Liu, X.; Chai, T., New approaches on \(\operatorname{H} \infty\) control of T-S fuzzy systems with interval time-varying delay, Fuzzy sets and systems, 160, 1669-1688, (2009) · Zbl 1175.93127
[13] 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, 750-762, (2009)
[14] Liu, F.; Wu, M.; He, Y.; Yokoyama, R., New delay-dependent stability criteria for T-S fuzzy systems with time-varying delay, Fuzzy sets and systems, 161, 2033-2042, (2010) · Zbl 1194.93117
[15] J.Y. An, G.L. Wen, W. Xu, Improved results on fuzzy \(\operatorname{H} \infty\) filter design for T-S fuzzy systems, Discrete Dynamics in Nature and Society 2010, 21 pp., doi: http://dx.doi.org/10.1155/2010/392915. · Zbl 1205.93040
[16] Yue, D.; Han, Q.L.; Lam, J., Network-based robust \(\operatorname{H} \infty\) control of systems with uncertainty, Automatica, 41, 999-1007, (2005) · Zbl 1091.93007
[17] F. Gouaisbaut, D. Peaucelle, Delay-dependent stability analysis of linear time delay systems, in: Proceedings of the IFAC TDC, 2006, pp. 5-7.
[18] Y. Ariba, F. Gouaisbaut, Delay-dependent stability analysis of linear systems with time-varying delay, in: Proceedings of the IEEE CDC, 2007, pp. 2053-2058.
[19] Zhang, X.-M.; Han, Q.-L., A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays, International journal of robust nonlinear control, 19, 1922-1930, (2009) · Zbl 1185.93106
[20] Zhang, X.-M.; Han, Q.-L., New lyapunov – krasovskii functionals for global asymptotic stability of delayed neural networks, IEEE transactions on neural networks, 20, 533-539, (2009)
[21] Boyd, S.; Ghaoui, L.E.; Feron, E., Linear matrix inequality in system and control theory, SIAM studies in applied mathematics, (1994), SIAM Philadelphia
[22] Petersen, I.R.; Hollot, C.V., A Riccati equation approach to the stabilization of uncertain linear systems, Automatica, 22, 397-411, (1986) · Zbl 0602.93055
[23] Shao, H., New delay-dependent criteria for systems with interval delay, Automatica, 45, 744-749, (2009) · Zbl 1168.93387
[24] He, Y.; Wang, Q.-G.; Xie, L.; Lin, C., Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE transactions on automatic control, 52, 293-299, (2007) · Zbl 1366.34097
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.