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Given a nonlinear system, the sector-nonlinearity methodology provides a systematic way of transforming it in an equivalent Takagi–Sugeno (T–S) model. However, such transformation is not unique: conservatism of shape-independent performance conditions in the form of linear matrix inequalities results in some models yielding better results than others. This paper provides some guidelines on choosing...
Results on systematic methodologies for obtaining progressively greater invariant sets of nonlinear systems within a region of interest are reported in this work. As with recent results on the subject, algorithms are developed that iteratively prove stability for larger regions by subtracting those already proved to be stable; this task is performed by an easy-to-implement procedure for piecewise...
This paper presents two methodologies intended to address the problem of constructing the most adequate Takagi-Sugeno representation of a nonlinear system with respect to a performance goal: maximum decay rate. Both approaches are based on coordinate transformations: the first one uses the Hessian of the system in an attempt to represent nonlinearities as sum of squares of independent variables; the...
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