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Relaxed Stability Conditions for Discrete-Time T–S Fuzzy Systems via Double Homogeneous Polynomial Approach

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Abstract

This paper deals with the problem of stability analysis for discrete-time Takagi–Sugeno (T–S) fuzzy systems. The double homogeneous polynomially parameter-dependent (DHPPD) Lyapunov function is proposed, which is expressed in the double homogeneous polynomial form not only of the membership functions but also of the state variables. Based on the DHPPD Lyapunov function, a relaxed stability condition is derived. Additionally, the complete square matricial representation of homogeneous polynomials is considered to further reduce the conservatism. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.

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Acknowledgements

This work was supported in part by the National Nature Science Foundation under Grants 61673215, 61403199, 61403178, the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities under Grant ZR2016JL025.

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Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Jun Chen, Shengyuan Xu & Qian Ma

  2. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, Shandong, China

    Guangming Zhuang

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  1. Jun Chen
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  2. Shengyuan Xu
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  3. Qian Ma
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  4. Guangming Zhuang
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Correspondence to Jun Chen.

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Chen, J., Xu, S., Ma, Q. et al. Relaxed Stability Conditions for Discrete-Time T–S Fuzzy Systems via Double Homogeneous Polynomial Approach. Int. J. Fuzzy Syst. 20, 741–749 (2018). https://doi.org/10.1007/s40815-017-0339-5

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  • DOI: https://doi.org/10.1007/s40815-017-0339-5

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