New results on static output feedback H ∞  control for fuzzy singularly perturbed systems: a linear matrix inequality approach

Authors

  • Jinxiang Chen,

    Corresponding author
    1. State Key Laboratory of Intelligence Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China
    • State Key Laboratory of Hybrid Process Industry Automation System and Equipment Technology, Automation Research and Design Institute of Metallurgical Industry, China Iron & Steel Research Institute Group, Beijing, China
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  • Yanguang Sun,

    1. State Key Laboratory of Hybrid Process Industry Automation System and Equipment Technology, Automation Research and Design Institute of Metallurgical Industry, China Iron & Steel Research Institute Group, Beijing, China
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  • Haibo Min,

    1. High-Tech Institute of Xi'an, Xi'an, Shanxi, China
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  • Fuchun Sun,

    1. State Key Laboratory of Intelligence Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China
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  • Yungui Zhang

    1. State Key Laboratory of Hybrid Process Industry Automation System and Equipment Technology, Automation Research and Design Institute of Metallurgical Industry, China Iron & Steel Research Institute Group, Beijing, China
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Correspondence to: Jinxiang Chen, New Materials Building, Room 3-332, No.76 Xueyuan Nanlu, Haidian, Beijing 100081, China.

E-mail: cjx720127@163.com

SUMMARY

This paper presents the novel approaches of designing robust fuzzy static output feedback H ∞  controller for a class of nonlinear singularly perturbed systems. Specifically, the considered system is approximated by a fuzzy singularly perturbed model. With the use of linear matrix inequality (LMI) methods, two methods are provided to design fuzzy static output feedback H ∞  controllers. The resulted controllers can guarantee that the closed-loop systems are asymptotically stable and satisfy H ∞  performances for sufficiently small ϵ. In contrast to the existing results, the proposed approaches have two advantages: (i) the gains of controller are solved directly by a set of ϵ-independent LMIs, and therefore, the problem of selecting the initial values in iterative LMIs algorithm can be avoided, and (ii) the smaller control input efforts are needed. The given methods are easy to implement and can be applied to both standard and nonstandard nonlinear singularly perturbed systems. Two numerical examples are provided to illustrate the effectiveness of the developed methods. Copyright © 2012 John Wiley & Sons, Ltd.

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