6533b7d5fe1ef96bd1264837

RESEARCH PRODUCT

Relaxed Stability and Performance LMI Conditions for Takagi-Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function Shapes

Carlos AriñoAntonio Sala

subject

Mathematical optimizationPolynomialApplied MathematicsPolynomial fuzzy systemsQuadratic stabilityLinear matrix inequalityFuzzy control systemNonlinear controlLinear matrix inequalityRelaxed conditionTakagi–Sugeno fuzzy controlDefuzzificationComputational Theory and MathematicsArtificial IntelligenceControl and Systems EngineeringRelaxed stabilityFuzzy numberParallel distributed compensationMembership functionMathematics

description

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.

yearjournalcountryeditionlanguage
2008-10-01
10.1109/tfuzz.2008.926585