Fuzzy-Affine-Model-Based Filtering Design for Continuous-Time Roesser-Type 2-D Nonlinear Systems

Meng Wang, Hak-Keung Lam, Jianbin Qiu, Huaicheng Yan, Zhichen Li

Abstract: This article tackles the problem of filtering design for continuous-time Roesser-type 2-D nonlinear systems via Takagi–Sugeno (T-S) fuzzy affine models. The aim is to design an admissible piecewise affine (PWA) filter such that the filtering error system is asymptotically stable with a prescribed disturbance attenuation level. First, 2-D Roesser nonlinear systems are approximated by a kind of 2-D fuzzy affine models with norm-bounded uncertainties. Then, the premise variable space of the 2-D fuzzy affine systems is partitioned into two classes of subspaces, that is: 1) crisp regions and 2) fuzzy regions. For each region, boundary continuity matrices and characterizing matrices are constructed by utilizing the space partition information and 2-D structure. After that, novel piecewise Lyapunov functions are constructed, based on which together with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> -procedure, the asymptotic stability with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal H_{\infty }$ </tex-math></inline-formula> performance is guaranteed for the filtering error system. By the projection lemma and some elegant convexification techniques, the PWA <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal H_{\infty }$ </tex-math></inline-formula> filtering design conditions are obtained. Finally, the less conservativeness and effectiveness of the proposed approach over a common Lyapunov function-based one are illustrated by simulation studies.