A Novel Fuzzy-Affine-Model-Based Finite Frequency Filtering Design for 2-D Nonlinear Systems

This work investigates the problem of piecewise affine (PWA) filtering design for two-dimensional (2-D) Roesser nonlinear systems with finite frequency performance based on Takagi–Sugeno (T–S) fuzzy affine models. The goal is to synthesize a 2-D PWA filter such that the resulting filtering error system is asymptotically stable and simultaneously satisfies a finite frequency $\mathscr{H}_{\infty}$ performance $\gamma$ . With the utilization of the state space partition knowledge on 2-D fuzzy models, a novel PWA filter is obtained. By exploiting the 2-D Fourier transform technique to convert 2-D disturbances into their frequency domain counterparts, finite frequency $\mathscr{H}_{\infty}$ performance analysis conditions are established, and then by applying projection lemma, an admissible frequency information-based filter design approach is proposed for 2-D Roesser nonlinear systems. Finally, the effectiveness of the PWA finite frequency filtering synthesis approach is validated through simulation studies on two examples.