Filter design for two-dimensional discrete-time T-S fuzzy systems described by FM LSS model

Abstract

This our work is concerned with the problem of filter design in two-dimensional (2D) discrete-time non-linear systems in Takagi-Sugeno (T-S) fuzzy model described by Fornasini-Marchesini local state-space (FM LSS) Model. The problem to be solved in the paper is to find a $H_{\infty}$ filter model such that the filtering error system is asymptotically stable and has a reduced $H_{\infty}$ performance index. Via the use of the Lyapunov functions approach and parameterize slack matrices, new design conditions guaranteeing the $H_{\infty}$ T-S fuzzy filter method of FM LSS model are developed by solving linear matrix inequalities (LMIs). At last, the simulation results are provided to show the effectiveness and the validity of the proposed T-S fuzzy of FM LSS model strategy by a practical application has been made.