Filter design for discrete-time two-dimensional T–S fuzzy systems with finite frequency specification

ABSTRACTThis paper deals with the filter design problem of two-dimensional (2-D) discrete-time nonlinear systems described by Fornasini–Marchesini local state–space (FM LSS) model under Takagi–Sugeno (T–S) fuzzy rules. The frequency of disturbance input is assumed to be known and to reside in a finite frequency (FF) range. A novel so-called FF l2 gain is defined for 2-D discrete-time systems, which extends the standard l2 gain. The aim of this paper is to design filters such that the filtering error system is asymptotically stable and has the disturbance attenuation performance in sense of FF l2 gain. Sufficient conditions for the existence of a desired fuzzy filter are established in terms of linear matrix inequalities (LMIs). Simulation examples demonstrate the technique and its advantage.