Robust stability analysis of TS-fuzzy-model-based control systems with both elemental parametric uncertainties and norm-bounded approximation error

JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing

Volumn 47, Issue 2, 2004, Pages 686-693

  Hsieh, Chen Huei ^a   Chou, Jyh Horng ^b  

^a CHIENKUO TECHNOLOGY UNIVERSITY   (Taiwan)

^b NATIONAL KAOHSIUNG UNIVERSITY OF APPLIED SCIENCES   (Taiwan)

Author keywords

Approximation error; Elemental parametric uncertainties; Linear matrix inequalities; Robust stability analysis; TS fuzzy model based control systems

Indexed keywords

APPROXIMATION THEORY; FUZZY CONTROL; MATRIX ALGEBRA; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; ROBUSTNESS (CONTROL SYSTEMS);

LINEAR MATRIX INEQUALITIES (LMI); PARAMETRIC UNCERTAINTIES; ROBUST STABILITY ANALYSIS; TAKAGI-SUGENO (TS) FUZZY MODEL;

CONTROL SYSTEMS;

CONTROL SYSTEM;

EID: 4644324640     PISSN: 13447653     EISSN: None     Source Type: Journal    
DOI: 10.1299/jsmec.47.686     Document Type: Article

References (21)

1. Boyd, S., Ghaoui, L.E., Feron, E. and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, (1994), SIAM, Philadelphia.
2. Babuska, R., Fuzzy Modeling for Control, (1998), Kluwer, Boston.
3. Chen, B.S., Tseng, C.S. and Uang, H.J., Robustness Design of Nonlinear Dynamic Systems via Fuzzy Linear Control, IEE Trans. Fuzzy Systems, Vol.7 (1999), pp. 571-585.
4. Chen, J. and Ren, Z., A Comparison of Small Gain versus Lyapunov Type Robust Stability Bounds, Int. J. of Robust and Nonlinear Control, Vol.11 (2001), pp.1407-1414.
5. Chou , J.H., Improved Measures of Stability Robustness for Linear Discrete Systems with Structured Uncertainties, Control Theory and Advanced Technology, Vol.10 (1995), pp.1169-1180.
6. Farinwata, S.S., Filev, D. and Langari, R., Fuzzy Control: Synthesis and Analysis, (2000), John Wiley & Sons, Chichester.
7. Feng, M. and Harris, C.J., Feedback Stabilization of Fuzzy Systems via Linear Matrix Inequalities, Int. J. of Systems Science, Vol.32 (2001), pp.221-231.
8. Gahinet, P., Nemirovski, A., Laub, A.J. and Chilai, M., LMI Control Toolbox, (1995), The Math Works Inc., Massachusetts.
9. Hsieh, C.H., Chou, J.H. and Wu, Y.J., Optimal Takagi-Sugeno Fuzzyin Schedular Design Using Taguchi-MHGA Method, JSME Int. J., Ser. C, Vol.44 (2001), pp. 143-155.
10. Kiriakidis, K., Non-Linear Control System Design via Fuzzy Modeling and LMIs, Int. J. Control, Vol.72 (1999), pp.676-685.
11. Lam, H.K., Leung, F.H.F. and Tam, P.K.S., Fuzzy Control of a Class of Multivariable Nonlinear Systems Subjct to Parameter Uncertainties: Model Reference Approach, Int. J. of Approximate Reasoning, Vol.226 (2001), pp.129-144.
12. Lee, H.J., Park, J.B. and Chen, G., Robust Fuzzy Control of Nonlinear Systems with Parametric Uncertainties, IEE Trans. Fuzzy Systems, Vol.9 (2001), pp.369-379.
13. Lee, K.R., Jeung, E.T. and Park, H.B., Robust Fuzzy H-Infinity Control for Uncertain Nonlinear Systems via State Feedback: An LMI Approach, Fuzzy Sets and Systems, Vol.120 (2001), pp.123-134.
14. Roberts, A.W. and Varberg, D.E., Convex Functions, (1973), Academic Press, New York.
15. Takagi, T. and Sugeno , M., Fuzzy Identification of Systems and Its Applications to Modeling and Control, IEE Trans, Systems, Man and Cybernetics, Vol.15 (1985), pp.116-132.
16. Tanaka, K., Ikeda, T. and Wang, H.O., Robust Stabilization of a Class of Uncertain Nonlinear Systems via Fuzzy Control: Quadratic Stabilizability, H-Infinity Control Theory and Linear Matrix I nequalities, IEEE Trans, Fuzzy Systems, Vol.4 (1996), pp.1-13.
17. Tanaka, K., Ikeda, T. and Wang, H.O., Fuzzy Regulators and Fuzzy Observers: Relaxed Stability Conditions and LMI-Based Designs, IEEE Trans . Fuzzy Systems, Vol.6 (1998), pp.250-265.
18. Tanaka, k., Hori, T. and Wang, H.O., An Integrated Fuzzy Control System Design for Nonlinear Systems, Proc. of the 38th Conf. on Decision and Control, Phoenix, Arizona, (1999), pp.4349-4354.
19. Tong, S., Wang, T. and Li, H.X., Fuzzy Robust Tracking Control for Uncertain Nonlinear Systems, Int.J. of Approximate Reasoning, Vol.30 (2002), pp.73-90.
20. Wang, H.O., Tanaka, K. and Griffin, M.F., An Approach to fuzzy Control of Nonlinear Systems: Stability and Design Issues, IEEE Trans. Fuzzy Systems, Vol.4 (1996), pp.14-223.
21. Weinmann, A., Uncertain Models and Robust Control, (1991), Springer-Verlag, Hongkong.