Reducing the number of vertices in some Takagi-Sugeno models: example in the mechanical field

International audience; This paper is concerned with the building of application-oriented model-based Takagi-Sugeno models that arise from sector nonlinearity methodology. Despite its exactness, this modeling technique produces a polytopic embedding with a number of vertices of 2 raised to the number of nonlinearities which, if high, represents a rapid growth in the number of linear matrix inequalities (needed to solve even the simplest control and observation schemes). A solution for model reduction is proposed based on the similarity of Taylor approximations amongst nonlinearities, with a measurable bound on the approximation, which - as proven with a suitable application example - brings the methodology closer to real-time demands.