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-frequencyl₂gain is defined that extends the standardl₂gain. Then, a sufficient condition for the filtering-error system with a finite-frequencyl₂gain 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.