Fuzzy frequency response: Proposal and application for uncertain dynamic systems

Fuzzy frequency response: proposal and application for uncertain dynamic systems is proposed in this paper. The uncertain dynamic system is partitioned into several linear sub-models, in terms of transfer function, and organized into Takagi–Sugeno (TS) fuzzy structure. The main contribution of this approach is demonstrated, from a Theorem, that the fuzzy frequency response is a bound in the magnitude and phase Bode plots. The analysis, from the fuzzy dynamic model, at low and high frequencies, is obtained varying the frequency ωω from zero to infinity.

► Fuzzy frequency response for uncertain systems from experimental data.
► Membership functions are generated by clustering algorithm.
► Linear sub-models are identified from least square method.
► Frequency response estimated from the equivalent Takagi–Sugeno fuzzy model.