An uncertain structure on Takagi-Sugeno fuzzy model

The main objective of the note is to study the coefficient structure involving firing strength that is imbedded in a model-based Takagi-Sugeno fuzzy control system. We discuss T-S models with two controllers involved: parallel distributed compensation (PDC) and non-PDC controllers. It is shown that either a quadratically dependent structure or a multilinearly dependent structure can appear. A polynomial geometry illustrating inclusion of families with aforementioned parametric structures is given by an example.