Open AccessH ∞ filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances
Author(s) -
Duan Zhaoxia,
Shen Jian,
Ghous Imran,
Fu Jinna
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5918
Subject(s) - control theory (sociology) , filter (signal processing) , filter design , mathematics , fuzzy control system , frequency domain , fuzzy logic , attenuation , discrete time and continuous time , regular polygon , computer science , control (management) , mathematical analysis , statistics , physics , geometry , artificial intelligence , optics , computer vision
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.