Subspace-Based Takagi–Sugeno Modeling for Improved LMI Performance

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 a sector-nonlinearity T-S model, with provable optimality (in a particular sense) in the case of quadratic nonlinearities. The approach is based on Hessian and restrictions of a function onto a subspace.