H∞ filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances. Issue 13 (31st July 2019)

• Record Type: Journal Article
• Authors: Duan, Zhaoxia; Shen, Jian; Ghous, Imran; Fu, Jinna
• Is Part Of: IET control theory & applications. Volume 13:Issue 13(2019)
• Page Start: 1983
• Page End: 1994
• Publication Date: 2019-07-31
• Subjects: discrete time systems -- asymptotic stability -- convex programming -- fuzzy systems -- H∞ filters -- nonlinear systems; discrete‐time 2D T–S fuzzy systems -- finite frequency disturbances -- filter design problem -- two‐dimensional discrete‐time nonlinear systems -- Takagi–Sugeno fuzzy model -- exogenous disturbances -- frequency‐domain characteristics -- filtering error system -- systematic filter design scheme -- gas absorption system -- H∞ filtering -- disturbance attenuation performance -- fuzzy filter design -- finite frequency domain -- convex optimisation problem -- FF H∞ performance index; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2018.5918
• Languages: English
• ISSNs: 1751-8644

Abstract

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.