Robust fuzzy control for continuous perturbed time-delay affine Takagi-Sugeno fuzzy models. (English) Zbl 1263.93127

Summary: The stability analysis and controller synthesis methodology for a continuous perturbed time-delay affine (CPTDA) Takagi-Sugeno (T-S) fuzzy model is proposed in this paper. The CPTDA T-S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and \(H_{\infty }\) performance constraints for the CPTDA T-S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach.


93C42 Fuzzy control/observation systems
93B35 Sensitivity (robustness)
93C73 Perturbations in control/observation systems
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[1] Chang, Fuzzy controller design via the inverse solution of Lyapunov equations, ASME, J. Dyn. Syst. Meas. Control 125 (1) pp 42– (2003)
[2] Chang, Passive fuzzy control with relaxed conditions for discrete affine T-S fuzzy systems, Int. J. Innov. Comp. Inf. Control 3 (4) pp 853– (2007)
[3] Chang, Analysis and synthesis of discrete nonlinear passive systems via affine T-S fuzzy models, Int. J. Syst. Sci. 39 (8) pp 809– (2008) · Zbl 1283.93160
[4] Chang, Constrained fuzzy controller design of discrete Takagi-Sugeno fuzzy models, Fuzzy Sets Syst. 133 (1) pp 37– (2003) · Zbl 1051.93057
[5] Chang, Discrete fuzzy control of time-delay affine Takagi-Sugeno fuzzy models with H constraint, IEE Proc. Control Theory Appl. 153 (6) pp 745– (2006)
[6] Chang, Synthesis of nonlinear discrete control systems via time-delay affine Takagi-Sugeno fuzzy models, ISA Transactions 44 (2) pp 243– (2005)
[7] Kim, Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI: Discrete case, IEEE Trans. Syst. Man Cybern. Part B 31 (1) pp 132– (2001)
[8] Kim, Stability analysis and synthesis for an affine fuzzy control system via LMI and ILMI: a continuous case, IEEE Trans. Fuzzy Syst. 10 (3) pp 391– (2002)
[9] Takagi, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cybern. 15 (1) pp 116– (1985) · Zbl 0576.93021
[10] Tanaka, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach (2001)
[11] Tanaka, Stability analysis and design of fuzzy control systems, Fuzzy Sets Syst. 45 (2) pp 135– (1992) · Zbl 0758.93042
[12] Wang, An approach to fuzzy control of nonlinear systems: stability and design issues, IEEE Trans. Fuzzy Syst. 4 (1) pp 14– (1996)
[13] Dugard, Stability and Control of Time-Delay Systems (1998) · Zbl 0901.00019
[14] Malek-Zavarei, Time-Delay Systems: Analysis, Optimization and Applications (1987) · Zbl 0658.93001
[15] Cao, Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach, IEEE Trans. Fuzzy Syst. 8 (2) pp 200– (2000)
[16] Guan, Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays, IEEE Trans. Fuzzy Syst. 12 (2) pp 236– (2004) · Zbl 1142.93363
[17] Qu, Robust Control of Nonlinear Uncertain Systems (1998)
[18] Stoorvogel, The H Control Problem (1992)
[19] Zhou, Robust and Optimal Control (1996)
[20] Boyd, Linear Matrix Inequalities in System and Control Theory (1994) · Zbl 0816.93004
[21] Cao, Stability analysis of linear time-delay systems subject to input saturation, IEEE Trans. Circuits Syst. Fundam. Theory Appl. 49 (2) pp 233– (2002) · Zbl 1368.93461
[22] Jankovic, Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems, IEEE Trans. Autom. Control 46 (7) pp 1048– (2001) · Zbl 1023.93056
[23] Zhang, Schur complements and matrix inequalities in the Lowner ordering, Linear Alg. Appl. 321 (1-3) pp 399– (2000) · Zbl 0977.15008
[24] Khalil, Nonlinear Systems (2000)
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