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An SOS-Based Observer Design for Discrete-Time Polynomial Fuzzy Systems

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Abstract

This paper investigates the polynomial fuzzy observer design for discrete-time uncertain polynomial systems. Three classes of discrete-time polynomial fuzzy systems are studied via a sum of squares (SOS) approach. A polynomial fuzzy system is a more general representation of the well-known Takagi–Sugeno (T–S) fuzzy system. The conditions in the proposed approach are derived in terms of SOS, which is the extension of the LMI method. Hence, the conditions obtained in this paper are more general than the corresponding LMI approaches for T–S fuzzy systems. All the design conditions in the proposed approach can be symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. Numerical examples are provided to demonstrate the validity and applicability of the proposed SOS-based design approach.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (61433004, 61273027), Science and Technology planning project of Liaoning Province, China (2013219005), and IAPI Fundamental Research Funds 2013ZCX14. This work was supported also by the development project of key laboratory of Liaoning province.

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Author notes

  1. Jianyu Zhang

    Present address: Department of Cultural Foundation, Guidaojiaotong Polytechnic Institute, Shenyang, 110023, Liaoning, China

Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, Liaoning, China

    Yingying Wang & Jianyu Zhang

  2. State Key Laboratory of Synthetical Automation for Process Industries, College of Information Science and Engineering, Northeastern University, Shenyang, 110819, Liaoning, China

    Huaguang Zhang & Yingchun Wang

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  1. Yingying Wang
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  2. Huaguang Zhang
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Correspondence to Huaguang Zhang.

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Wang, Y., Zhang, H., Zhang, J. et al. An SOS-Based Observer Design for Discrete-Time Polynomial Fuzzy Systems. Int. J. Fuzzy Syst. 17, 94–104 (2015). https://doi.org/10.1007/s40815-015-0003-x

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  • DOI: https://doi.org/10.1007/s40815-015-0003-x

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