Asymptotically necessary and sufficient stability with respect to nonquadratic Lyapunov function for Takagi-Sugeno model

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2009, Pages 4162-4167

  Ding, Baocang ^a   Zou, Tao ^b  

^a CHONGQING UNIVERSITY   (China)

^b ZHEJIANG UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

MODAL ANALYSIS; STATE FEEDBACK;

COMMON QUADRATIC LYAPUNOV FUNCTION; NECESSARY AND SUFFICIENT STABILITY CONDITIONS; NON-QUADRATIC LYAPUNOV FUNCTIONS; PARAMETER DEPENDENTS; STABILITY CONDITION; STATE FEEDBACK LAWS; TAKAGI-SUGENO; TAKAGI-SUGENO MODELING;

LYAPUNOV FUNCTIONS;

EID: 77950823128     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2009.5400013     Document Type: Conference Paper

References (16)

1. B. Ding, "Poly-quadratic stability of discrete-time nonlinear systems in Takagi-Sugeno's form", Asian Journal of Control, to be published, 2009.
2. B. Ding, H. Sun and Y. Qiao, "Stability analysis of T-S fuzzy control systems base-on parameter-dependent Lyapunov function", ACTA AUTOMATICA SINICA, vol.31, 2005, pp 651-654.
3. B. Ding, H. Sun and P. Yang, "Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno's form", Automatica, vol.42, 2006, pp 503-508.
4. B. Ding and B. Huang, "Reformulation of LMI-based stabilisation conditions for non-linear systems in Takagi-Sugeno's form", International Journal of Systems Science, vol.39, 2008, pp 487-496.
5. B. Ding and B. Huang, "Stabilization of Takagi-Sugeno model via non-parallel distributed compensation law", in Proceedings of the 7th World Congress on Intelligent Control and Automation, Chongqing, China, 2008, pp. 724-729.
6. G. Feng, "Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions", IEEE Transactions on Fuzzy Systems, vol.12, 2004, pp 22-28.
7. C.H. Fang, Y.S. Liu, S.W. Kau, L. Hong and C.H. Lee, "A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems", IEEE Transactions on Fuzzy Systems, vol.14, 2006, pp 386-397.
8. T.M. Guerra and L. Vermeiren, "LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form", Automatica, vol.40, 2004, pp 823-829.
9. E. Kim and H. Lee, "New approaches to relaxed quadratic stability condition of fuzzy control systems", IEEE Transactions on Fuzzy Systems, vol.8, 2000, pp 523-533.
10. X.D. Liu and Q.L. Zhang, "New approaches to H-infinity controller designs based on fuzzy observers for T-S fuzzy systems via LMI", Automatica, vol.39, 2003, pp 1571-1582.
11. V.F. Montagner, R.C.L.F. Oliveira and P.L.D. Peres, "Necessary and sufficient LMI conditions to compute quadratically stabilizing state feedback controllers for Takagi-Sugeno systems", in Proceedings of the American Control Conference, NY, USA, 2007, pp. 4059-4064.
12. R.C.L.F. Oliveira and P.L.D. Peres, "Parameter-dependent LMIs in robust analysis: characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations", IEEE Transactions on Automatic Control, vol.52, 2007, pp 1334-1340.
13. A. Sala and C. Arino, "Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Application of Polya's theorem", Fuzzy Sets and Systems, vol.158, 2007, pp 2671-2686.
14. K. Tanaka, T. Hori and H.O. Wang, "A multiple Lyapunov function approach to stabilization of fuzzy control systems", IEEE Transactions on Fuzzy Systems, vol.11, 2003, pp 582-589.
15. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control", IEEE Transactions on Systems, Man and Cybernetics, vol.15, 1985, pp 116-132.
16. H.O. Wang, K. Tanaka and M. Griffin, "An approach to fuzzy control of nonlinear systems: stability and design issues", IEEE Transactions on Fuzzy Systems, vol.4, 1996, pp 14-23.