Filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances

Abstract

This study investigates the filter design problem for two-dimensional (2D) discrete-time non-linear systems in Takagi–Sugeno (T–S) fuzzy model. The frequency of the exogenous disturbances is assumed to belong to a known finite frequency (FF) domain. An FF performance is defined for 2D discrete-time systems, which generalises the standard one and makes use of the frequency-domain characteristics of practical signals. By virtue of the defined FF performance, sufficient conditions are proposed for analysing the disturbance attenuation performance of the filtering error system. Efficient conditions are obtained to guarantee the existence of a filter and such that the error system is asymptotically stable with an FF performance index. A systematic filter design scheme is developed by converting the corresponding fuzzy filter design into a convex optimisation problem. Finally, a gas absorption system is employed to illustrate the validity of the proposed methods.