Quadratic Inequalities over Affine T-S Fuzzy Models

Abstract

While the affine T-S fuzzy model is much more effective for describing the dynamics of the system concerned in comparison with the regular T-S fuzzy model, it encounters some difficulties when designing a controller based on the model because of the affine term within. However the difficulties can be overcome by introduction of a kind of quadratic inequalities. This paper proposes a way to yield such quadratic inequalities based on the information over the antecedent part of affine T-S fuzzy model rules. Although the introduction of such quadratic inequalities is motivated by controller designs based on the affine T-S fuzzy model, the way of the introduction can be applied to other fuzzy models.