Choosing a Takagi-Sugeno model for improved performance

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 second one takes into account the direction provided by a “failing” eigenvector with respect to the desired performance acting on the linearization of the system. It is shown that, in some respects, both methodologies offer better solutions than ordinary “blind” TS modeling.