Relaxed Stability and Performance LMI Conditions for Takagi-Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function Shapes
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http://dx.doi.org/10.1109/TFUZZ.2008.926585 |
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Title
Relaxed Stability and Performance LMI Conditions for Takagi-Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function ShapesDate
2008Publisher
Institute of Electrical and Electronics EngineersISSN
1063-6706Type
info:eu-repo/semantics/articleSubject
Abstract
Most linear matrix inequality (LMI) fuzzy control
results in literature are valid for any membership function, i.e.,
independent of the actual membership shape. Hence, they are conservative
(with respect to other ... [+]
Most linear matrix inequality (LMI) fuzzy control
results in literature are valid for any membership function, i.e.,
independent of the actual membership shape. Hence, they are conservative
(with respect to other nonlinear control approaches) when
specific knowledge of the shapes is available. This paper presents
relaxed LMI conditions for fuzzy control that incorporate such
shape information in the form of polynomial constraints, generalizing
previous works by the authors. Interesting particular cases
are overlap (product) bounds and ellipsoidal regions. Numerical
examples illustrate the achieved improvements, as well as the possibilities
of solving some multiobjective problems. The results also
apply to polynomial-in-membership Takagi–Sugeno fuzzy systems [-]
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