H∞ filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances. Issue 13 (31st July 2019) - Duan, Zhaoxia; Shen, Jian; Ghous, Imran; Fu, Jinna
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 H ∞ 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 H ∞ 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 H ∞ 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.