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access icon free filtering for discrete-time 2D T–S fuzzy systems with finite frequency disturbances

  • Author(s): Zhaoxia Duan 1 ; Jian Shen 2 ; Imran Ghous 3 ; Jinna Fu 1
    • View affiliations
  • Source: Volume 13, Issue 13, 03 September 2019, p. 1983 – 1994
    DOI:  10.1049/iet-cta.2018.5918 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 17/08/2018, Accepted 07/06/2019, Revised 22/12/2018, Published 07/06/2019

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.

Inspec keywords: H∞ filters; asymptotic stability; convex programming; fuzzy systems; discrete time systems; nonlinear systems

Other keywords: H∞ filtering; discrete-time 2D T–S fuzzy systems; systematic filter design scheme; Takagi–Sugeno fuzzy model; disturbance attenuation performance; filter design problem; gas absorption system; finite frequency domain; fuzzy filter design; finite frequency disturbances; convex optimisation problem; frequency-domain characteristics; FF H∞ performance index; filtering error system; exogenous disturbances; two-dimensional discrete-time nonlinear systems

Subjects: Nonlinear control systems; Discrete control systems; Stability in control theory; Fuzzy control; Signal processing theory; Optimisation techniques

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