Transformation of fuzzy Takagi-Sugeno models into piecewise affine models

Fuzzy modeling of dynamical systems can be viewed as an interpolation of a collection of linear models where the interpolation coefficients depend on set membership functions. The fuzzy interference applies only when the membership functions intersect otherwise only one model is valid. The approach presented in this paper models the intersections with an uncertainty measure reducing the overall fuzzy model to Piecewise Affine (PWA) description, over-approximating the original fuzzy model. Once such an approximation is calculated, existing algorithms can be applied which yield controllers guaranteeing closed-loop stability. Since the PWA model over-approximates a given fuzzy model, if such a controller is calculated, it guarantees stability of the original fuzzy model as well.