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Non-fragile Observer-Based \({\varvec{H_\infty}} \) Control for Switched Takagi–Sugeno Fuzzy Systems Using Past Output Measurements

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Abstract

This paper pays attention to the non-fragile observer-based \(H_\infty \) control problem of switched Takagi-Sugeno (T–S) fuzzy systems, where every subsystem is described by the T–S fuzzy model with local nonlinear terms. Different from the existing observer-based control strategy, a distinguishing feature of this paper is that constructed observers can make full use of current and past output measurements to enhance the performance of the observers in state estimation. However, the introduction of past output measurements has brought challenges to stability analysis and controller design. To tackle these difficulties and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. First, a new non-fragile observer-based \(H_\infty \) control criterion is deduced based on the fuzzy Lyapunov function method. Then, the method of simultaneously solving observer and controller gains is obtained by introducing free matrix variables and using the linear matrix inequality approach. This solving method is more efficient than the traditional two-step method. Finally, two confirmatory instances are given.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on a reasonable request.

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Funding

This work was supported by the Natural Science Research Project of Colleges and Universities of Anhui Province (Grant No. 2023AH040123), the Open Research Fund of Anhui Key Laboratory of Detection Technology and Energy Saving Devices (Grant No. JCKJ2022A05), and the National Natural Science Foundation of China (Grant Nos. 61803001, 62363005, 62273005).

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Authors and Affiliations

  1. Anhui Key Laboratory of Detection Technology and Energy Saving Devices, Anhui Polytechnic University, Wuhu, 241000, P. R. China

    Zhongzhang Xiao, Qunxian Zheng & Xinya Mao

  2. School of Electrical Engineering, Anhui Polytechnic University, Wuhu, 241000, P. R. China

    Zhongzhang Xiao, Qunxian Zheng & Xinya Mao

  3. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, P. R. China

    Xiang Wu

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  1. Zhongzhang Xiao
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Contributions

Zhongzhang Xiao: Conceptualization, Writing-original draft, Formal analysis, Software, Validation. Qunxian Zheng: Funding acquisition, Methodology, Resources, Supervision, Writing-review and editing. Xinya Mao: Visualization. Xiang Wu: Reviewing.

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Correspondence to Qunxian Zheng.

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Xiao, Z., Zheng, Q., Mao, X. et al. Non-fragile Observer-Based \({\varvec{H_\infty}} \) Control for Switched Takagi–Sugeno Fuzzy Systems Using Past Output Measurements. Int. J. Fuzzy Syst. 26, 2658–2674 (2024). https://doi.org/10.1007/s40815-024-01753-9

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