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

ABSTRACT

This paper is concerned with $H_{\mathrm{\infty }}$ 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 $r^2$ 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 $H_{\mathrm{\infty }}$ 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.

Keywords:

• 2-D T–S fuzzy systems
• discrete stochastic systems
• fault detection
• computational complexity

Acknowledgments

This work was supported by National Natural Science Foundation of China (No. 61903244).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 61903244].

Notes on contributors

Xiaofeng Li

Xiaofeng Li received the Ph.D. degree in control science and engineering from Nanjing University of Science and Technology in 2015. She is currently working in Faculty of Mathematics and Physics, Huaiyin Institute of Technology. Her current research interests include fuzzy system control and switched systems.

Lizhen Li

Lizhen Li received the Ph.D. degree in control science and engineering from Nanjing University of Science and Technology in 2013. She is currently a lecturer with the Department of Mathematics and Physics, Shanghai University of Electric Power. Her current research interests include fuzzy systems control and multidimensional networked control systems.

Shuxia Ye

Shuxia Ye received her BS degree from Xinyang Normal University, China, in 1998. She received MS and PhD degree from Nanjing University of Science and Technology, China, in 2007 and 2011, majoring in Automatic Control. Her research interests are in the areas of 2-D systems, time delay systems and nonlinear systems.