A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems

This paper proposes a new quadratic stabilization condition for Takagi-Sugeno (T-S) fuzzy control systems. The condition is represented in the form of linear matrix inequalities (LMIs) and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2006-06, Vol.14 (3), p.386-397
Main Authors: Fang, Chun-Hsiung, Liu, Yung-Sheng, Kau, Shih-Wei, Hong, Lin, Lee, Ching-Hsiang
Format: Article
Language:English
Subjects:
Control system synthesis
Control systems
Controllers
Design engineering
Dynamical systems
Fuzzy
Fuzzy control
Fuzzy feedback controller
Fuzzy logic
Fuzzy set theory
Fuzzy systems
Linear matrix inequalities
linear matrix inequality
Nonlinear control systems
Nonlinear systems
Output feedback
relaxed quadratic stability
Stability
Stabilization
State feedback
Studies
Takagi-Sugeno (T-S) fuzzy systems
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Summary:This paper proposes a new quadratic stabilization condition for Takagi-Sugeno (T-S) fuzzy control systems. The condition is represented in the form of linear matrix inequalities (LMIs) and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature. A rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases. In comparison with conventional conditions, the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design. The latter design work is quite hard for T-S fuzzy control systems. Based on the LMI-based conditions derived, one can easily synthesize controllers for stabilizing T-S fuzzy control systems. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous-time nonlinear system.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2006.876331