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This paper introduces a novel approach for stability analysis and controller design of nonlinear models, both continuous- and discrete-time, based on an exact piecewise Takagi–Sugeno representation which generalizes the sector nonlinearity methodology. The motivation behind this work lies on the fact that piecewise-induced Takagi–Sugeno representations have smaller variations than single ones covering the whole modeling area, thus increasing the chances of finding piecewise solutions for stability analysis or controller synthesis. Moreover, this relaxation is shown to produce progressively better estimations of the domain of attraction via easy-to-implement algorithms that demand much less computational effort than other recent approaches in the literature. Examples are provided to highlight the advantages of the contributions over the existing methods.