Fuzzy Filter Design for Nonlinear Systems in Finite-Frequency Domain

This paper is concerned with the problem of fuzzy-filter design for discrete-time nonlinear systems in the Takagi-Sugeno (T-S) form. Different from existing fuzzy filters, the proposed ones are designed in finite-frequency domain. First, a so-called finite-frequency l₂ gain is defined that extends the standard l₂ gain. Then, a sufficient condition for the filtering-error system with a finite-frequency l₂ gain is derived. Based on the obtained condition, three fuzzy filters are designed to deal with noises in the low-, middle-, and high-frequency domain, respectively. The proposed fuzzy-filtering method can get a better noise-attenuation performance when frequency ranges of noises are known beforehand. An example about a tunnel-diode circuit is given to illustrate its effectiveness.