Further Results on Sampled-Data $H_{\infty }$ Filtering for T–S Fuzzy Systems With Asynchronous Premise Variables

This article presents a new sampled-data fuzzy filter design method for Takagi–Sugeno fuzzy systems with the asynchronous premise variables. In the new fuzzy filter design method, the membership functions of the filter are affine transformed by scaling and biasing the system’s membership functions. Taking the advantage of the newly proposed method, the asynchronous problem of the premise variables between the system and filter is easily resolved. Based on the looped function and a modified free-weighting matrix inequality, the sampled system’s output is handled, and the filter design condition is formulated in terms of a parameterized linear matrix inequality with affine matched fuzzy parameter vectors. Additionally, a modified Finsler’s lemma is devised to handle the affine matched fuzzy parameter vectors. By utilizing the relationship between the transformed membership functions, the filter design condition for $H_{\infty }$ performance is enhanced with larger allowable maximum bounds of variable sampling intervals. Lastly, the superiority of the presented method is verified by comparing the numerical simulations with existing methods.