Generalized nonlinear sector approaches for Takagi-Sugeno models

The Nonlinear Sector Approach (NLSA) is a way to construct Takagi-Sugeno (T-S) models which exactly represent nonlinear systems with bounded nonlinearities. Generally, the nonlinearities are bounded by a box-shaped set, however, this paper generalizes the NLSA for polytopic and smooth convex bounding sets, providing new ways of reducing the intrinsic conservatism of T-S representations with interdependent scheduling parameters. Some Linear Matrix Inequalities (LMI) criteria for stability analysis of these models are provided throughout the paper.