Constrained fuzzy controller design of discrete Takagi-Sugeno fuzzy models

Fuzzy Sets and Systems

Volumn 133, Issue 1, 2003, Pages 37-55

  Chang, Wen Jer ^a   Sun, Chein Chung ^b  

^a NATIONAL TAIWAN OCEAN UNIVERSITY   (Taiwan)

^b NATIONAL CENTRAL UNIVERSITY   (Taiwan)

Author keywords

Discrete Takagi Sugeno fuzzy systems; Generalized inverse theory; Observability Gramian; Singular value decomposition

Indexed keywords

FEEDBACK CONTROL; LINEAR CONTROL SYSTEMS; LYAPUNOV METHODS; ROBUSTNESS (CONTROL SYSTEMS);

FUZZY SYSTEMS;

FUZZY CONTROL;

EID: 0037213785     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(02)00276-2     Document Type: Article

References (33)

1. Ben-Israel A., Greville T.N.E. Generalized Inverses: Theory and Application. 1974;Wiley, New York.
2. Boyd S. et al. Linear Matrix Inequalities in Systems and Control Theory. 1994;SIAM, Philadelphia, PA.
3. Campbell S.L., Meyer C.D. Generalized Inverses of Linear Transformations. 1991;Dover, New York.
4. Chang W.J. Model-based fuzzy controller design with common observability Gramian assignment. ASME, J. Dyn. Syst. Meas. Control. 123:2001;113-116.
5. W.J. Chang, C.C. Sun, Fuzzy control with common observability Gramian assignment for continuous Takagi-Sugeno models, Proc. 1999 American Control Conference, San Diego, CA, 1999, pp. 1366-1370.
6. Cheng C.M., Rees N.W. Stability analysis of fuzzy multivariable systems. vector Lyapunov function approach IEE Proc. Part D. 144:1997;403-412.
7. Joh J., Chen Y.H., Langari R. On the stability issues of linear Takagi-Sugeno fuzzy models. IEEE Trans. Fuzzy Syst. 6:1998;402-410.
8. Joh J., Langari R., Jeung E.T., Chung W.J. A new design method for continuous Takagi-Sugeno fuzzy controller with pole placements. an LMI approach IEEE Internat. Conf. Systems, Man, Cybernet. 3:1997;2969-2974.
9. J. Joh, Y. Nam, S.K. Hong, W.J. Chung, On the systematic design of Takagi-Sugeno fuzzy control systems, Internat. ICSC Symp. on Engineering of Intelligent Systems: EIS'98, Tenerife, Spain, 1998, pp. 113-119.
10. Johnson C.R., Lundquist M. An inertia formula for Hermitian matrices with sparse inverses. Linear Algebra Appl. 162:1992;541-556.
11. Kailath T. Linear Systems. 1980;Prentice-Hall, Englewood Cliffs, NJ.
12. Kim S., Cho Y., Park M. A multirule-base controller using the robust property of a fuzzy controller and its design method. IEEE Trans. Fuzzy Syst. 4:1996;315-327.
13. K. Kiriakidis, A. Grivas, A. Tzes, A sufficient criterion for stability of the Takagi-Sugeno fuzzy model, Proc. Fifth Internat. Fuzzy Systems Conference, New Orleans, LA, 1996, pp. 277-282.
14. Lu W.S., Wang H.P., Antoniou A. An efficient method for the evaluation of the controllability and observability Gramians of 2-D digital filters and systems. IEEE Trans. Circuits and Systems - II: Analog Digital Signal Process. 39:1992;695-704.
15. Narendra K.S., Balakrishnan J. A common Lyapunov function for stable LTI systems with commuting. A -matrices IEEE Trans. Automat. Control. 39:1994;2469-2471.
16. Sreeram V., Agathoklis P. Discrete-system reduction via impulse-response Gramians and its relation to q-Markov covers. IEEE Trans. Automat. Control. 37:1992;653-658.
17. Takagi T., Sugeno M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Systems, Man, Cybernet. SMC-15:1985;116-132.
18. ∞ control theory, and linear matrix inequalities IEEE Trans. Fuzzy Syst. 4:1996;1-13.
19. Tanaka K., Ikeda T., Wang H.O. Fuzzy regulator and fuzzy observers. relaxed stability conditions and LMI-based designs IEEE Trans. Fuzzy Syst. 6:1998;250-265.
20. Tanaka K., Sano M. A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer. IEEE Trans. Fuzzy Syst. 2:1994;119-134.
21. K. Tanaka, M. Sano, On the concepts of regulator and observer of fuzzy control systems, Proc. Third Internat. Fuzzy Systems Conf., Orlando, FL, 1994, pp. 767-772.
22. Tanaka K., Sano M. Trajectory stabilization of a model car via fuzzy control. Fuzzy Sets and Systems. 70:1995;155-170.
23. Tanaka K., Sugeno M. Stability analysis and design of fuzzy control systems. Fuzzy Sets and Systems. 45:1992;135-156.
24. Thathachar M.A.L., Viswanath P. On the stability of fuzzy systems. IEEE Trans. Fuzzy Syst. 5:1997;145-151.
25. Vetter W.J. Matrix calculus operations and Taylor expansions. SIAM Rev. 15:1973;352-369.
26. Vetter W.J. Vector structures and solutions of linear matrix equations. Linear Algebra Appl. 10:1975;181-188.
27. H.O. Wang, K. Tanaka, An LMI-based stable fuzzy control of nonlinear systems and its application to control of chaos, Proc. Fifth Internat. Fuzzy Systems Conf., New Orleans, LA, 1996, pp. 1433-1438.
28. Wang H.O., Tanaka K., Griffin M.F. An approach to fuzzy control of nonlinear systems. stability and design issues IEEE Trans. Fuzzy Syst. 4:1996;14-23.
29. M.A. Wicks, R.A. Decarlo, An energy approach to controllability, Proc. 27th Conf. on Decision and Control, Austin, TX, 1988, pp. 2072-2077.
30. Wicks M.A., Decarlo R.A. Gramian assignment based on the Lyapunov equation. IEEE Trans. Automat. Control. 35:1990;465-468.
31. Xu J.H., Skelton R.E. An improved covariance assignment theory for linear discrete systems. IEEE Trans. Automat. Control. 37:1992;1588-1591.
32. Yasuda K., Skelton R.E. Assigning controllability and observability Gramians in feedback control. J. Guidance Control Dyn. 14:1991;878-885.
33. Yedavalli R.K. Perturbation bounds for robust stability in linear state space models. Internat. J. Control. 42:1985;1507-1517.