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GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function

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Abstract

Generalized H 2 (GH 2) stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH 2 stability sufficient conditions are derived in terms of linear matrix inequalities (LMIs). The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.

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Authors and Affiliations

  1. School of Science, Xidian University, Xi’an, 710071, PRC

    Zhi-Le Xia & Jun-Min Li

  2. School of Mathematics and Information Engineering, Taizhou University, Taizhou, 317000, PRC

    Zhi-Le Xia

Authors
  1. Zhi-Le Xia
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  2. Jun-Min Li
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Corresponding author

Correspondence to Zhi-Le Xia.

Additional information

Zhi-Le Xia received the B. Sc. degree in the Department of Mathematics at Huaiyin Normal University, PRC in 2003, and the M. Sc. degree in the Department of Applied Mathematics at Xidian University, PRC in 2006. He is currently a Ph.D. candidate in the Department of Applied Mathematics at Xidian University, PRC.

His research interests include robust control, fuzzy control, and time-delay control systems.

Jun-Min Li received the B. Sc. and M. Sc. degrees from the Department of Applied Mathematics at Xidian University, PRC in 1987 and 1989, respectively, and the Ph.D. degree in systems engineering from Xi’an Jiaotong University, PRC in 1997. He is currently a professor in the Department of Applied Mathematics at Xidian University, PRC.

His research interests include robust and adaptive control, optimal control, iterative learning control, and networked control systems.

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Xia, ZL., Li, JM. GH 2 control for uncertain discrete-time-delay fuzzy systems based on a switching fuzzy model and piecewise Lyapunov function. Int. J. Autom. Comput. 6, 261–266 (2009). https://doi.org/10.1007/s11633-009-0261-x

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  • DOI: https://doi.org/10.1007/s11633-009-0261-x

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