# zbMATH — the first resource for mathematics

Delay-range-dependent robust stabilization for uncertain T-S fuzzy control systems with interval time-varying delays. (English) Zbl 1242.93067
Summary: This paper is concerned with robust stabilization for a class of T – S fuzzy control systems with interval time-varying delays. An approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities. The main points of the approach are: (i) two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria; (ii) an appropriate Lyapunov – Krasovskii functional is constructed by including both the lower and upper bounds of the interval time-varying delays; and (iii) neither model transformation nor free weighting matrices are employed in the theoretical result derivation. As a result, some improved sufficient stability criteria are derived, and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed approach.

##### MSC:
 93C42 Fuzzy control/observation systems 93D21 Adaptive or robust stabilization
Full Text:
##### References:
 [1] 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, 2, 213-229, (2001) · Zbl 1002.93051 [2] Chen, B.; Liu, X.P., Delay-dependent robust H_∞ control for T-S fuzzy systems with time delay, IEEE transactions on fuzzy systems, 13, 4, 544-556, (2005) [3] Chen, B.; Liu, X.P.; Tong, S.C., New delay-dependent stabilization conditions of T-S fuzzy systems with constant delay, Fuzzy sets and systems, 158, 20, 2209-2224, (2007) · Zbl 1122.93048 [4] Fang, C.H.; Liu, Y.S.; Kau, S.W.; Hong, L.; Lee, C.H., A new LMI based approach to relaxed quadratic stabilization of T-S fuzzy control systems, IEEE transactions on fuzzy systems, 14, 3, 386-397, (2006) [5] Garcı´a-Nieto, S.; Salcedo, J.; Martı´nez, M.; Laurı´, D., Air management in a diesel engine using fuzzy control techniques, Information sciences, 179, 19, 3392-3409, (2009) · Zbl 1171.93346 [6] Ghaoui, L.E.; Oustry, F.; AitRami, M., A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE transactions on automatic control, 42, 8, 1171-1176, (1997) · Zbl 0887.93017 [7] Gu, K.; Kharitonov, V.L.; Chen, J., Stability of time-delay systems, (2003), Birkhauser · Zbl 1039.34067 [8] Guan, X.P.; Chen, C.L., Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays, IEEE transactions on fuzzy systems, 12, 2, 236-249, (2004) · Zbl 1142.93363 [9] Han, Q.-L., New results for delay-dependent stability of linear systems with time-varying delay, International journal of systems sciences, 33, 3, 213-228, (2002) · Zbl 1031.93138 [10] Han, Q.-L.; Gu, K., Stability of linear systems with time-varying delay: A generalized discretized Lyapunov functional approach, Asian journal of control, 3, 3, 170-180, (2001) [11] He, Y.; Wang, Q.-G.; Lin, C.; Wu, M., Delay-range-dependent stability for system with time-varying delay, Automatica, 43, 2, 371-376, (2007) · Zbl 1111.93073 [12] Hespanha, J.P.; Naghshtabrizi, P.; Xu, Y., A survey of recent results in networked control systems, Proceeding of the IEEE, 95, 1, 138-162, (2007) [13] Jiang, X.; Han, Q.-L., Delay-dependent robust stability for uncertain linear systems with interval time-varying delay, Automatica, 42, 6, 1059-1065, (2006) · Zbl 1135.93024 [14] Jiang, X.; Han, Q.-L., Robust H_∞ control for uncertain takagi – sugeno fuzzy systems with interval time-varying delay, IEEE transactions on fuzzy systems, 15, 2, 321-331, (2007) [15] Li, C.G.; Wang, H.J.; Liao, X.F., Delay-dependent robust stability of uncertain fuzzy systems with time varying delays, IEE Proceedings: control theory and applications, 151, 4, 417-421, (2004) [16] Lien, C.; Yu, K.; Chen, W.; Wan, Z.; Chung, Y., Stability criteria for uncertain takagi – sugeno fuzzy systems with interval time-varying delay, IET control theory and applications, 1, 3, 764-769, (2007) [17] 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 [18] Peng, C.; Tian, Y.-C., State feedback controller design of networked control systems with interval time-varying delay and nonlinearity, International journal of robust and nonlinear control, 18, 12, 1285-1301, (2008) · Zbl 1284.93111 [19] 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, 20, 2713-2729, (2008) · Zbl 1170.93344 [20] Peng, C.; Yue, D.; Tian, Y.-C., New approach on robust delay-dependent H_∞ control for uncertain T-S fuzzy systems with interval time-varying delay, IEEE transactions on fuzzy systems, 17, 4, 890-900, (2009) [21] Peng, C.; Yue, D.; Yang, T.C.; Tian, E.G., On delay-dependent approach to robust stability and stabilization for T-S fuzzy systems with constant delay and uncertainties, IEEE transactions on fuzzy systems, 17, 5, 1143-1156, (2009) [22] Peng, C.; Tian, Y.-C., Delay-dependent robust H_∞ control for uncertain systems with time-varying delay, Information sciences, 179, 18, 3187-3197, (2009) · Zbl 1171.93016 [23] Precup, R.; Preitl, S.; Korondi, P., Fuzzy controllers with maximum sensitivity for servosystems, IEEE transactions on industrial electronics, 54, 3, 1298-1310, (2007) [24] Sanchez, E.; Becerra, H.; Velez, C., Combining fuzzy PID and regulation control for an autonomous mini-helicopter, Information sciences, 177, 10, 1999-2022, (2007) [25] Takagi, T.; Sugeno, M., Fuzzy identification of its applications to modeling and control, IEEE transactions on systems, man and cybernetics, 15, 1, 116-132, (1985) · Zbl 0576.93021 [26] Tian, E.G.; Peng, C., Delay dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay, Fuzzy sets and systems, 157, 4, 544-559, (2006) · Zbl 1082.93031 [27] Wang, R.J.; Lin, W.W.; Wang, W.J., Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems, IEEE transactions on systems, man and cybernetics, 34, 2, 1288-1292, (2004) [28] Wang, Y.; Tanaka, K.; Bushnell, L., Fuzzy control of nonlinear time-delay systems: stability and design issues, () [29] Wu, H.N.; Cai, K.Y., Robust fuzzy control for uncertain discrete-time nonlinear Markovian jump systems without mode observations, Information sciences, 177, 6, 1509-1522, (2007) · Zbl 1120.93337 [30] Wu, H.N.; Li, H.X., New approach to delay-dependent stability analysis and stabilisation for continuous time fuzzy systems with time-varying delay, IEEE transactions on fuzzy systems, 15, 3, 482-493, (2007) [31] Yoneyama, J., New robust stability conditions and design of robust stabilizing controllers for takagi – sugeno fuzzy time-delay systems, IEEE transactions on fuzzy systems, 15, 5, 828-839, (2007) [32] Yoneyama, J., Robust stability and stabilization for uncertain takagi – sugeno fuzzy time-delay systems, Fuzzy sets and systems, 158, 2, 115-134, (2007) · Zbl 1110.93033 [33] Yue, D.; Han, Q.-L.; Peng, C., State feedback controller design of networked control systems, IEEE transactions on circuits and systems II: express briefs, 51, 11, 640-644, (2004) [34] Yue, D.; Han, Q.-L.; Lam, J., Network-based robust H_∞ control of systems with uncertainty, Automatica, 41, 6, 999-1007, (2005) · Zbl 1091.93007
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.