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

Author

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  • Zhaoxia Duan
  • Jun Zhou
  • Jian Shen

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.

Suggested Citation

  • Zhaoxia Duan & Jun Zhou & Jian Shen, 2019. "Filter design for discrete-time two-dimensional T–S fuzzy systems with finite frequency specification," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(3), pages 599-613, February.
    • Handle: RePEc:taf:tsysxx:v:50:y:2019:i:3:p:599-613
    DOI: 10.1080/00207721.2018.1564086
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