Finite-Frequency Model Reduction of Takagi–Sugeno Fuzzy Systems

This paper considers the model-reduction problem for continuous-time Takagi–Sugeno (T–S) fuzzy systems. Different from existing full-frequency methods, a finite-frequency model-reduction method is proposed in this paper. The proposed method can get a better approximation performance when input signals belong to a finite-frequency domain. To this end, a finite-frequency
$H_\infty$
performance index is first defined. Then, a sufficient finite-frequency performance analysis condition is derived by the aid of Parseval's theorem and quadratic functions. Based on this condition and projection lemma, three model-reduction algorithms for T–S fuzzy systems with input signals in low-frequency, middle-frequency, and high-frequency domain are obtained, respectively. Finally, an example is given to illustrate the effectiveness of the proposed method.