Abstract
The robust \(H_{\infty }\) filtering problem is solved here for two-dimensional (2-D) Takagi–Sugeno fuzzy systems, focusing on designing T–S filters such that the filtering error system is asymptotically stable and guarantees a prescribed attenuation of the noise. The methodology is based on using basis-dependent Lyapunov functions and slack matrix variables, which makes it possible to eliminate products between Lyapunov and system matrices. A linear matrix inequality (LMI)-based approach is proposed, which makes it possible to design filters for nonlinear systems, as illustrated by examples that also show the effectiveness of the proposed approach and its reduced conservatism.
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Benzaouia, A., Hmamed, A., Tadeo, F. (2016). Robust \(H_{\infty }\) Filtering of Two-Dimensional Takagi–Sugeno Fuzzy Systems. In: Two-Dimensional Systems. Studies in Systems, Decision and Control, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-20116-0_10
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DOI: https://doi.org/10.1007/978-3-319-20116-0_10
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