Optimal-Performance Takagi-Sugeno Models via the LMI Null Space*

The problem of achieving optimal performance for nonlinear systems by constructing the most adequate exact Takagi-Sugeno model of the plant and considering its relationship with the linear matrix inequalities it gives raise to, is considered in this report. In contrast with recent approaches on the subject, the performance goal can be chosen from a wide variety of definitions while constraints are no longer required to be state-dependent. As before, this approach is based on coordinate transformations that isolate the effects of the system nonlinearities and allow optimisation with respect to some performance level, by keeping some norm close enough to the linearised performance. It is shown that the proposed methodology outperforms both ordinary “blind” TS modeling as well as former similar approaches.