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H∞ fault detection for 2-D T–S discrete stochastic fuzzy systems

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  • Xiaofeng Li
  • Lizhen Li
  • Shuxia Ye

Abstract

This paper is concerned with $H_\infty $H∞ fault detection (FD) problem for a class of two-dimensional (2-D) Takagi–Sugeno (T–S) discrete stochastic fuzzy systems. Based on the parallel distributed compensation (PDC), the fuzzy FD filter and the dynamics of FD system are constructed. Since the multiplicative property of the FD system would drastically increase the number of the stability conditions, a method of decoupling based on dimension expansion is used. By decoupling, the number of LMI-based stability conditions is reduced to r from $r^2 $r2 by the conventional method. Then, the fuzzy FD filter is designed. The corresponding fuzzy FD system is proved to be mean-square asymptotically stable and satisfies the $H_\infty $H∞ attenuation level for all disturbances. In addition, a theorem is proposed to prove that the stability conditions based on decoupling method are equivalent to those of conventional method. Finally, simulation examples are provided to demonstrate the usefulness of the proposed design methods.

Suggested Citation

  • Xiaofeng Li & Lizhen Li & Shuxia Ye, 2020. "H∞ fault detection for 2-D T–S discrete stochastic fuzzy systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(12), pages 2258-2275, September.
    • Handle: RePEc:taf:tsysxx:v:51:y:2020:i:12:p:2258-2275
    DOI: 10.1080/00207721.2020.1793233
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