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Stability analysis and controller synthesis for fuzzy descriptor systems

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  • Chih-Peng Huang

Abstract

This article primarily investigates the stability and controller design of fuzzy descriptor systems. The standard Takagi–Sugeno (T–S) fuzzy model is generalised into a descriptor T–S fuzzy model with the distinct derivative matrices in each rule, which can be used to represent a larger class of nonlinear systems. Based on a derived equivalent stability condition for the nominal descriptor system, the stability of unforced fuzzy descriptor systems with blending different derivative matrices can be treated. Furthermore, parallel distributed compensation (PDC) and a fuzzy proportional and derivative state feedback (PDSF) controller are proposed for stabilising the resulting closed-loop fuzzy descriptor systems. Significantly, all the presented criteria are formulated in terms of linear matrix inequalities (LMIs), so the stability analysis or a stabilising fuzzy controller can be readily achieved via current LMI solvers. Given numerical examples, we demonstrate the effectiveness and merit of the proposed approach.

Suggested Citation

  • Chih-Peng Huang, 2013. "Stability analysis and controller synthesis for fuzzy descriptor systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(1), pages 23-33.
    • Handle: RePEc:taf:tsysxx:v:44:y:2013:i:1:p:23-33
    DOI: 10.1080/00207721.2011.577248
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    Cited by:

    1. Xin-zhuang Dong, 2014. "Admissibility analysis of linear singular systems via a delta operator method," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(11), pages 2366-2375, November.
    2. Xin-Rong Yang & Guo-Ping Liu, 2016. "Admissible consensus for heterogeneous descriptor multi-agent systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(12), pages 2869-2877, September.
    3. Chen Zheng & Jinde Cao & Manfeng Hu & Xiaozheng Fan, 2017. "Finite-time stabilisation for discrete-time T–S fuzzy model system with channel fading and two types of parametric uncertainty," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(1), pages 34-42, January.
    4. Mu, Yunfei & Zhang, Huaguang & Su, Hanguang & Wang, Yingchun, 2021. "Robust normalization and H∞ stabilization for uncertain Takagi-Sugeno fuzzy singular systems with time-delays," Applied Mathematics and Computation, Elsevier, vol. 388(C).

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