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Design of Non-fragile Controller for Singular Fractional Order Takagi–Sugeno Fuzzy Systems

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Abstract

This paper investigates the stabilization problem of a class of singular fractional order fuzzy systems with order \(0<\alpha <1\). Firstly, by the method of full rank decomposition of matrix, equality constraint of admissibility criterion in most existing literature is eliminated. Next, we present a stabilization criterion for singular fractional order Takagi–Sugeno (T–S) fuzzy systems by designing non-fragile state feedback controllers. Then, applying an equivalent form of original system in admissibility, the non-fragile output feedback controllers are designed to guarantee the closed-loop systems stable. And for fractional order \(1<\alpha <2\) case, using similar designing approaches, strict linear matrix inequality (LMI) stabilization criteria based on non-fragile state and output feedback controller are obtained. Finally, two numerical simulation examples are given to illustrate the effectiveness of the proposed method.

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  1. School of Sciences, Northeastern University, Shenyang, 110819, Liaoning, China

    Xuefeng Zhang & Kaijing Jin

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  1. Xuefeng Zhang
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  2. Kaijing Jin
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Correspondence to Xuefeng Zhang.

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Zhang, X., Jin, K. Design of Non-fragile Controller for Singular Fractional Order Takagi–Sugeno Fuzzy Systems. Int. J. Fuzzy Syst. 22, 1289–1298 (2020). https://doi.org/10.1007/s40815-020-00822-z

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  • DOI: https://doi.org/10.1007/s40815-020-00822-z

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