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Observer-Based Fuzzy Control of Uncertain Nonlinear Singular Systems under Multi-Performance Requirements

Author

Listed:
  • Wen-Jer Chang

    (Department of Marine Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan)

  • Yu-Min Huang

    (Department of Marine Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan)

  • Yann-Horng Lin

    (Department of Marine Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan)

Abstract

This paper discusses an observer-based fuzzy control problem for uncertain nonlinear singular systems under Multi-Performance Requirements (MPRs). The approach used in the paper is to model the system using a Takagi–Sugeno (T-S) fuzzy model that can be analyzed using linear control theories. The proposed control scheme is based on the Parallel Distributed Compensation (PDC) approach and Proportional Derivative (PD) control scheme. The goal is to design an observer-based fuzzy controller that achieves stability of the system and also satisfies the Guarantee Cost Control (GCC) constraint while maintaining a desired passive constraint. The stability analysis is performed using Lyapunov theory, and the sufficient conditions are transformed into a Linear Matrix Inequality (LMI) form using a Shur Complement, free-weighting matrix method and Singular Value Decomposition (SVD) techniques. The LMI conditions are then solved using convex optimization algorithms. Finally, the proposed control method is validated using a bio-economic system to demonstrate its effectiveness.

Suggested Citation

  • Wen-Jer Chang & Yu-Min Huang & Yann-Horng Lin, 2023. "Observer-Based Fuzzy Control of Uncertain Nonlinear Singular Systems under Multi-Performance Requirements," Mathematics, MDPI, vol. 11(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2632-:d:1167102
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    References listed on IDEAS

    as
    1. Hao Wang & Zhaoliang Sheng & Chong Lin & Bing Chen, 2022. "Asymmetric Lyapunov–Krasovskii functional method for admissibility analysis and stabilisation of T-S fuzzy singular systems with time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(14), pages 2998-3009, October.
    2. 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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