Filter design for discrete-time two-dimensional T–S fuzzy systems with finite frequency specification

Zhaoxia Duan, Jun Zhou and Jian Shen

International Journal of Systems Science, 2019, vol. 50, issue 3, 599-613

Abstract: This paper deals with the filter design problem of two-dimensional (2-D) discrete-time nonlinear systems described by Fornasini–Marchesini local state–space (FM LSS) model under Takagi–Sugeno (T–S) fuzzy rules. The frequency of disturbance input is assumed to be known and to reside in a finite frequency (FF) range. A novel so-called FF $ l_2 $ l2 gain is defined for 2-D discrete-time systems, which extends the standard $ l_2 $ l2 gain. The aim of this paper is to design filters such that the filtering error system is asymptotically stable and has the disturbance attenuation performance in sense of FF $ l_2 $ l2 gain. Sufficient conditions for the existence of a desired fuzzy filter are established in terms of linear matrix inequalities (LMIs). Simulation examples demonstrate the technique and its advantage.

Date: 2019
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DOI: 10.1080/00207721.2018.1564086

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