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

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 urn:x-wiley:17518644:media:cth2bf00489:cth2bf00489-math-0002 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 urn:x-wiley:17518644:media:cth2bf00489:cth2bf00489-math-0003 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 urn:x-wiley:17518644:media:cth2bf00489:cth2bf00489-math-0004 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.