On the local interpretation of Takagi-Sugeno fuzzy models from a dynamical systems view

Takagi-Sugeno (TS) fuzzy models have been the popular choice for multi-model based nonlinear system identification for controller design. However, the interpretation of the model from a dynamical systems point of view is still unclear. We investigate the interpretation of the TS fuzzy models in terms of local dynamics of nonlinear systems in state space. The investigation is based on the comparison between the constant-affine recursive i/o equation and constant-affine state space representations. We show that the true local dynamics is not identifiable by TS fuzzy models by analysis and example. For the identification of constant-affine state space models, a subspace identification algorithm is proposed to identify the true local dynamics with zero initial conditions