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Observer-based -control for discrete-time T–S fuzzy systems

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  • Xiao-Heng Chang
  • Guang-Hong Yang
  • Haibo Wang

Abstract

This article further studies the observer-based H∞-control problem for discrete-time Takagi–Sugeno (T–S) fuzzy systems. By using fuzzy Lyapunov functions and introducing slack variables, a sufficient condition, which can guarantee observer-based H∞-control performance for T–S fuzzy systems, is proposed in terms of a set of bilinear matrix inequalities. Moreover, in the so-called two-step procedure, results of the first step are allowed to select in order to reduce the conservatism of previous approaches. In comparison with the existing literature, the proposed approach not only provides more relaxed H∞-control conditions but also ensures better H∞-control performance. Finally, the validity and applicability of the proposed approach are successfully demonstrated through two numerical examples.

Suggested Citation

  • Xiao-Heng Chang & Guang-Hong Yang & Haibo Wang, 2011. "Observer-based -control for discrete-time T–S fuzzy systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(10), pages 1801-1809.
    • Handle: RePEc:taf:tsysxx:v:42:y:2011:i:10:p:1801-1809
    DOI: 10.1080/00207721003653708
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    Cited by:

    1. Thanh Binh Nguyen & Hyoung-Kyu Song, 2022. "Further Results on Robust Output-Feedback Dissipative Control of Markovian Jump Fuzzy Systems with Model Uncertainties," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    2. Mohammad Hassan Asemani & Vahid Johari Majd, 2015. "A robust -tracking design for uncertain Takagi–Sugeno fuzzy systems with unknown premise variables using descriptor redundancy approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(16), pages 2955-2972, December.
    3. Guolin Hu & Jian Zhang & Zhiguo Yan, 2022. "Local H ∞ Control for Continuous-Time T-S Fuzzy Systems via Generalized Non-Quadratic Lyapunov Functions," Mathematics, MDPI, vol. 10(19), pages 1-13, September.
    4. R. Rakkiyappan & A. Chandrasekar & S. Lakshmanan, 2016. "Stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2247-2263, July.
    5. Zhiguo Yan & Zhiwei Zhang & Guolin Hu & Baolong Zhu, 2022. "Observer-Based Finite-Time H ∞ Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model," Mathematics, MDPI, vol. 10(12), pages 1-15, June.
    6. Sohaira Ahmad & Muhammad Rehan & Anas Ibrar & Muhammad Umair Ali & Amad Zafar & Seong Han Kim, 2024. "Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays," Mathematics, MDPI, vol. 12(9), pages 1-35, April.

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